arXiv subjects

Olivier Bénichou

Publications and source records attributed to Olivier Bénichou.

At least 19 recordsLinked to original sources

arXiv2026

Exact Microscopic One-Body Reduction in the Symmetric Exclusion Process

The symmetric exclusion process (SEP) is a paradigmatic model of interacting particle transport. Its current--density correlations are governed by an infinite many-body hierarchy of equations. Only recently, this hierarchy was found to collapse at large scales onto a single closed equation. Is this remarkable simplification created by coarse graining, or does it reflect a deeper property already present in the microscopic dynamics? Here we show that the second scenario is realized. At arbitrary time on the lattice, the entire hierarchy collapses onto a single linear equation which is exactly equivalent to a persistence problem for a single auxiliary random walker. Thus an interacting many-body problem reduces exactly to a genuine one-body problem before any scaling limit is taken. This reduction determines the complete finite-time correlation profile, including during nonequilibrium relaxation. More broadly, the microscopic operator uncovered here opens a route to more general correlation functions in the SEP, and may point to a general organizing principle for nonequilibrium interacting particle systems.

cond-mat.stat-mech↗

arXiv2026

Transverse geometry reshapes current and tracer fluctuation amplitudes in quasi-one-dimensional single files

Single-file transport means no overtaking: particles move in a narrow channel while preserving their longitudinal order. This simple constraint has profound dynamical consequences, most notably tracer subdiffusion, and has made single-file transport a paradigmatic form of confined many-body motion, observed from molecular transport in zeolites to single-file diffusion of colloids in narrow channels. A common modelling approach assumes that, once overtaking is suppressed, finite-width effects can be discarded or represented by an effective particle size in a strictly one-dimensional model. Starting from the Brownian dynamics in the full confined geometry, we instead derive the exact large-scale one-dimensional fluctuating-hydrodynamic equation governing the coarse-grained line density. Its transport coefficients are fixed by the confined equilibrium equation of state, through which the transverse geometry remains encoded in the one-dimensional description. Consequently, transverse geometry leaves the $t^{1/2}$ single-file scaling unchanged but can qualitatively reshape the density dependence of the current and tracer fluctuation amplitudes. In the minimal hard-core setting, this yields a collective diffusivity that can become non-monotonic in density for sufficiently wide no-passing channels. This geometric non-monotonicity propagates to exact large-scale predictions for the amplitudes of integrated-current fluctuations and tracer-displacement fluctuations. The effect is robust to the interaction potential, channel geometry, initial preparation and microscopic dynamics. Quasi-one-dimensional single-file transport therefore defines a distinct regime in which forbidding overtaking does not erase geometry from collective transport.

cond-mat.stat-mech↗

arXiv2026

Exact Nonlinear Active Microrheology in Diffusive Single-File Systems

Active microrheology probes a crowded medium by forcing a tracer and measuring its response. In single-file transport, where particles cannot overtake, a constant force $F$ produces a subballistic displacement $\langle X_t\rangle\simeq \sqrt{t}\,ξ(F)$ together with a persistent bath deformation. Despite decades of work, the exact nonlinear response at arbitrary force has remained confined to a few special solvable models. Here we remove this restriction by combining recent advances in hydrodynamic transport coefficients, a pressure-balance formulation of the local drive, and single-file duality, which eliminates the resulting moving boundary. This yields a closed exact boundary-value problem for general diffusive single files, determining both $ξ(F)$ and the full density profile. For overdamped Brownian particles with general interactions, all microscopic interaction details enter only through the equilibrium equation of state, bringing realistic interacting systems, including finite-width quasi-one-dimensional channels, within exact reach. The solution also reveals universal global laws; in particular, the bath-density dipole is fixed by the applied force independently of the interaction potential.

cond-mat.stat-mech↗

arXiv2026

Large volume statistics of first-passage observables of $d$-dimensional Jump Processes

First-passage observables (FPO) are central to understanding stochastic processes in confined domains, with applications spanning chemical reaction kinetics, foraging behavior, and molecular transport. While extensive analytical results exist for continuous processes, discrete jump processes - crucial for describing empirically observed dynamics - remain largely unexplored in this context. This paper presents a comprehensive framework to systematically evaluate FPO for $d$-dimensional isotropic jump processes, in the asymptotic regime of large confining domains, capturing both geometric and dynamical observables. Leveraging the connection between jump processes and their continuous counterparts, we address the limitations of continuous approximations in capturing discrete effects, particularly near absorbing boundaries. Our method unifies FPO calculations across edge and bulk regimes, providing explicit asymptotic expressions for key observables, such as splitting probabilities, distributions of escape points, and first-passage time distributions in complex geometries. We illustrate our approach with paradigmatic examples, including splitting probabilities in two-dimensional eccentric disks and mean exit times for heavy-tailed processes. These results underscore the broad applicability of our framework to diverse physical systems, offering novel insights into the complexity of discrete dynamics in bounded geometries.

cond-mat.stat-mech↗

arXiv2026

Exact collective first-passage statistics of N trail-interacting walkers

Memory encoded in the environment mediates interactions between active agents, from trail-following organisms to synthetic active matter depositing persistent tracks. Although such memory is known to strongly affect transport, its consequences for collective first-passage phenomena remain largely unexplored. Here we study $N$ one-dimensional random walkers interacting through a shared trail field. We characterize the $k^{\rm th}$ (among $N$) arrival time at a fixed target, and the probability that exactly $k$ walkers in $[0,1]$ reach one boundary before the other. For the broad class of self-interacting walkers with a saturating response to the trail, we derive exact expressions for the corresponding persistence exponents and splitting probabilities. Strikingly, despite the strong history-dependent correlations generated by the common environment, splitting probabilities are exactly identical whether walkers explore simultaneously or one after another. This invariance breaks down for nonsaturating trail interactions. Our results follow from an exact representation of the collective trail field and establish a framework for first-passage phenomena in systems coupled through persistent environmental memory.

cond-mat.stat-mech↗

arXiv2026

Universal fluctuations of first discoveries in competitive exploration

Random exploration is usually quantified by how fast new space is found, from the range of a single walker to the territory collectively covered by many walkers. In competitive exploration, first arrival secures an exclusive resource, as when foragers compete for food items or agents capture distributed targets. It is then no longer enough to know which sites have been discovered: one must determine, for each discovered site, which searcher reached it first. We introduce the discovery share $X_n$, the fraction of the first $n$ collective discoveries secured by a tagged searcher. For two identical competitors, exchange symmetry fixes $\langle X_n\rangle=1/2$, but the central question is whether this equal split emerges in each long exploration history or only on average, i.e. whether early competitive advantages are erased or persist. Here we show that the answer is controlled by the spectral dimension $d_s$, defined by the large-time decay of the probability that a single searcher is at its starting point after $t$ steps, $p_0(t)\sim t^{-d_s/2}$. Across ordinary diffusion, long-range superdiffusion and subdiffusion induced by crowding or memory, $d_s$ separates persistent randomness in recurrent exploration $(d_s<2)$, anomalously slow non-Gaussian concentration for $2\le d_s<3$, and Gaussian concentration, logarithmically corrected at $d_s=3$, for $d_s\ge3$. For $d_s\ge2$, we derive exact asymptotic variances, including prefactors, and the discovery scale on which competitive imbalances are erased. Two-point correlations of first-discovery labels identify the memory mechanism behind these regimes. The same phase structure persists under changes in geometry, competitor heterogeneity, number of competitors and memory, revealing a general fluctuation theory of first-arrival inequalities.

cond-mat.stat-mech↗

arXiv2026

A shortcut through the macroscopic fluctuation theory: a generalised Fick law

The macroscopic fluctuation theory is a powerful tool to characterise the large scale dynamical properties of diffusive systems, both in- and out-of-equilibrium. It relies on an action formalism in which, at large scales, the dynamics is fully determined by the minimum of the action. Within this formalism, the analysis of the statistical properties of a given observable reduces to solving the Euler-Lagrange equations with the appropriate boundary conditions. One must then compute the action at its minimum to deduce the cumulant generating function of the observable. This typically involves computing multiple integrals of cumbersome expressions. Recently, a simple formula has been conjectured to shortcut this last step, and compute the cumulant generating function of different observables (integrated current or position of a tracer) without the need to compute any integral. In this work, we prove this simple formula, and extend it to more general observables. We then illustrate the efficiency of this approach by applying it to compute the variance of a generalised current in the semi-infinite symmetric exclusion process and the joint properties of two occupation times in any diffusive system. In the case of the integrated current, our formula can be interpreted as a generalisation of Fick's law to obtain all the cumulants of the current beyond the average value.

cond-mat.stat-mech↗

arXiv2026

Macroscopic fluctuation theory of interacting Brownian particles

We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the collective diffusion coefficient, the MFT gives access to the exact large-scale dynamical properties of the system, both in- and out-of-equilibrium. In particular, we obtain exact results for dynamical correlations between the density and the current of particles. For one-dimensional systems, this allows us to obtain a precise description of these correlations for emblematic models, such as the Calogero and Riesz gases, and for systems with nearest-neighbor interactions such as the Rouse chain of hardcore particles or the recently introduced model of tethered particles. Tracer diffusion with the single-file constraint (but for arbitrary pairwise interaction) is also studied. For higher-dimensional systems, we quantitatively characterize these dynamical correlations by relying on standard methods such as the virial expansion.

cond-mat.stat-mech↗

arXiv2026

Number of local minima in discrete-time fractional Brownian motion

The analysis of local minima in time series data and random landscapes is essential across numerous scientific disciplines, offering critical insights into system dynamics. Recently, Kundu, Majumdar, and Schehr derived the exact distribution of the number of local minima for a broad class of Markovian symmetric walks [Phys. Rev. E \textbf{110}, 024137 (2024)]; however, many real-world systems are non-Markovian, typically due to interactions with possibly hidden degrees of freedom. This work investigates the statistical properties of local minima in discrete-time samples of fractional Brownian motion (fBm), a non-Markovian Gaussian process with stationary increments, widely used to model complex, anomalous diffusion phenomena. We derive a complete asymptotic characterization of the fluctuations of the number of local minima $m_N$ in an $N$-step discrete-time fBm. We show that the fluctuations of $m_N$ exhibit a sharp transition at the Hurst exponent $H=3/4$: for $H\le 3/4$ they satisfy a central limit theorem with Gaussian limiting law, whereas for $H>3/4$ they converge to a non-Gaussian Rosenblatt process. The convergence at the process level gives us full statistical description at all times. We exemplify it on the covariance of the rescaled minima process, which displays two qualitatively distinct regimes matching Brownian and Rosenblatt covariances on either side of this threshold. Our analysis relies on a Hermite/Wick decomposition of the local-minimum indicator, which isolates a quadratic functional of an effective long-memory mode as the unique driver of the anomalous statistics. These results identify the count of local minima as a simple and robust diagnostic of long-range dependence in non-Markovian Gaussian processes, a conclusion supported by numerical simulations.

cond-mat.stat-mech↗

arXiv2025

Beyond the Arcsine Law: Exact Two-Time Statistics of the Occupation Time in Jump Processes

Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and Lévy processes. By contrast, two-time occupation statistics, which directly probe temporal correlations and aging, have resisted exact characterization beyond renewal processes. In this Letter we derive exact results for generic one-dimensional jump processes, a central framework for intermittent and discretely sampled dynamics. Using generalized Wiener-Hopf methods, we obtain the joint distribution of occupation time and position, the aged occupation-time law, and the autocorrelation function. In the continuous-time scaling limit, universal features emerge that depend only on the tail of the jump distribution, providing a starting point for exploring aging transport in complex environments.

cond-mat.stat-mech↗

arXiv2025

Probing and modeling cell-cell communication in 2D biomimetic tissues

In tissues, cells in direct physical contact with each other can exchange ions or molecules via protein clusters called gap junctions that form channels across the membranes of adjacent cells. Here, we use a simplified biomimetic approach, coupled with theoretical modeling, to unravel the physical mechanisms controlling such transport. Tissues are mimicked with 2D hexagonal networks of monodisperse aqueous droplets connected by lipid membranes called Droplet Interface Bilayers (DIBs), decorated with $α$-Hemolysin ($α$HL) transmembrane proteins forming nanopores through heptamerization in the membrane. The diffusion of calcein across 2D DIB networks is thoroughly studied using epifluorescence microscopy at various $α$HL concentrations. The results are successfully confronted with a Continuous Time Random Walk model in hexagonal networks, with an average waiting time increasing nonlinearly with the concentration of pore monomers.

cond-mat.soft↗

arXiv2025

Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation

Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation. This equation remains mostly formal and linearization (or higher-order expansions) is required to obtain explicit expressions for physical observables, with a range of validity not easily defined. Here, by combining macroscopic fluctuation theory with equilibrium statistical mechanics, we provide a systematic alternative to the Dean--Kawasaki framework to characterize large-scale correlations. This approach enables us to obtain explicit and exact results for dynamical observables such as tracer cumulants and bath-tracer correlations in one dimension, both in and out of equilibrium. In particular, we reveal a generic non-monotonic spatial structure in the response of the bath following a temperature quench. Our approach applies to a broad class of interaction potentials and extends naturally to higher dimensions.

cond-mat.stat-mech↗

arXiv2025

Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems

Quantifying the correlations between the position of a tagged tracer and the density of surrounding bath particles is crucial for understanding tracer diffusion in interacting particle systems, and for characterizing the response properties of the bath. We address this problem analytically for both hard-core and soft-core interactions, using minimal yet paradigmatic models in $d$ spatial dimensions. In both cases, we derive analytical expressions for the spatial correlation profiles in the reference frame of the tracer. We reveal unexpected universal features in their large-distance behavior, characterized by power-law tails with exponents that depend solely on the spatial dimensionality of the system. Beyond these simple models, we demonstrate the robustness of our results across different regimes using particle-based numerical simulations.

cond-mat.stat-mech↗

arXiv2025

Tracer and current fluctuations in driven diffusive systems

Interacting particles diffusing in single-file is a fundamental model of transport in narrow channels where particles cannot bypass each other. An important result has been obtained by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)] for the mean square displacement of a tracer for any single-file model. It applies to any diffusive system, in particular the notable classes of colloidal systems and diffusive stochastic lattice gases. Since then, no analog result has been obtained in the important case where the particles are driven by an external field. Here, we fill this gap and determine the fluctuations and the skewness of the tracer's position for any driven diffusive system. In addition, we also consider a variety of important observables such as the integrated current, the response of the system to the perturbation induced by the displacement of the tracer, and the correlations between several tracers. Furthermore, we also unveil fundamental relations underlying the out-of-equilibrium dynamics of driven diffusive systems. This work constitutes a step toward the determination of the full distribution of all these observables in driven one-dimensional systems of interacting particles.

cond-mat.stat-mech↗

arXiv2025

Flips Reveal the Universal Impact of Memory on Random Explorations

Quantifying space exploration is a central question in random walk theory, with direct applications ranging from animal foraging, diffusion-limited reactions, and intracellular transport to stock markets. In particular, the explored domain by one or many simple memoryless (or Markovian) random walks has received considerable attention . However, the physical systems mentioned above typically involve significant memory effects, and so far, no general framework exists to analyze such systems. We introduce the concept of a \emph{flip}, defined most naturally in one dimension, where the visited territory is $[x_{\rm min}, x_{\rm max}]$: a flip occurs when, after discovering a new site at $x_{\rm max}$, the walker next discovers $x_{\rm min} - 1$ instead of $x_{\rm max} + 1$ (and vice-versa). While it reduces to the classical splitting probability in Markovian systems, we show that the flip probability serves as a key observable for quantifying the impact of memory effects on space exploration. Here, we demonstrate that the flip probability follows a strikingly simple and universal law: it decays inversely with the number of sites visited, as $1/n$, independently of the underlying stochastic process. We confirm this behavior through simulations across paradigmatic non-Markovian models and observe it in real-world systems, without relying on model assumptions, including biological tracer motion, DNA sequences, and financial market dynamics. Finally, we reveal the physical mechanism behind this universality and show how it extends to higher-dimensional and fractal domains. Our determination of universal flip statistics lay the groundwork for understanding how memory effects govern random explorations.

cond-mat.stat-mech↗

arXiv2025

Full stochastic dynamics of a tracer in a dense single-file system

Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of such a tracer has been well studied, with a known subdiffusive dynamics and a Gaussian description for the rescaled position, the finer details of multi-time correlations remain poorly understood. This work focuses on the limit where almost all sites of a Symmetric Exclusion Process (SEP), a paradigmatic lattice model, are occupied. It extends beyond Gaussian descriptions and single-time statistics to address the multi-time correlation functions of the tracer in the SEP. In this dense limit, we present a general relation between all $n$-time correlations of the non-Markovian tracer position process and the conditional probabilities of a single Markovian random walker. Using this relation, we derive explicit expressions for the four-time correlations and further explore important extensions: multiple tracers, non-equilibrium situations, and finite observation times. Our results underscore significant memory effects, strong temporal correlations, and the influence of initial conditions on long-time dynamics.

cond-mat.stat-mech↗

arXiv2025

Dynamics of soft interacting particles on a comb

We study the dynamics of overdamped Brownian particles interacting through soft pairwise potentials on a comb-like structure. Within the linearized Dean-Kawasaki framework, we characterize the particle density fluctuations by computing their one- and two-point correlation functions. For a tracer particle constrained to move along the comb backbone, we determine the spatial correlation profile between its position and the density of surrounding bath particles. Furthermore, we derive the correction to the diffusion coefficient of the tracer due to interactions with other particles, validating our results through numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry

The symmetric simple exclusion process (SEP) is a paradigmatic model of transport, both in and out-of-equilibrium. In this model, the study of currents and their fluctuations has attracted a lot of attention. In finite systems of arbitrary dimension, both the integrated current through a bond (or a fixed surface), and its fluctuations, grow linearly with time. Conversely, for infinite systems, the integrated current displays different behaviours with time, depending on the geometry of the lattice. For instance, in 1D the integrated current fluctuations are known to grow sublinearly with time, as $\sqrt{t}$. Here we study the fluctuations of the integrated current through a given lattice bond beyond the 1D case by considering a SEP on higher-dimensional lattices, and on a comb lattice which describes an intermediate situation between 1D and 2D. We show that the different behaviours of the current originate from qualitatively and quantitatively different current-density correlations in the systems, which we compute explicitly.

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