arXiv subjects

Yann Lanoiselée

Publications and source records attributed to Yann Lanoiselée.

9 recordsLinked to original sources

arXiv2026

A unifying approach to diffusive transport in annealed heterogeneous media

We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for elaborating, analyzing and classifying anomalous diffusion models in annealed heterogeneous media. This formulation incorporates correlations in the displacements together with correlated fluctuations of their amplitudes. Most known models of anomalous diffusion (including continuous-time random walk, fractional Brownian motion, and Lévy flights) and random diffusivity can be described and further generalized within this framework. Moreover, the unified view identifies the main statistical properties to be probed experimentally for a reliable classification of diffusive dynamics. The proposed matrix formulation facilitates the computation of the first four moments and allows for a systematic statistical characterization of the considered processes. The necessary and sufficient conditions are provided for the emergence of anomalous diffusion. General expressions for the non-Gaussian parameter, the ergodicity breaking parameter and the covariance of squared increments are derived. An expression for the characteristic function and the codifference (i.e., a generalized measure of correlations) are obtained and used to study the special cases of Lévy flights and Laplace motion with correlated displacements. Potential applications of this framework for systematic analysis and biophysical interpretations of experimental single-particle trajectories are discussed.

physics.bio-ph↗

arXiv2025

Super-resolved anomalous diffusion: deciphering the joint distribution of anomalous exponent and diffusion coefficient

The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^α$. Motivated by experiments reporting populations of the anomalous diffusion parameters $α$ and $D$, we aim to disentangle their respective contributions to the observed variability when this last is due to a true population of these parameters and when it arises due to finite-duration recordings. We introduce estimators of the anomalous diffusion parameters on the basis of the time-averaged mean squared displacement and study their statistical properties. By using a copula approach, we derive a formula for the joint density function of their estimations conditioned on their actual values. The methodology introduced is indeed universal, it is valid for any Gaussian process and can be applied to any quadratic time-averaged statistics. We also explain the experimentally reported relation $D\propto\exp(αc_1+c_2)$ for which we provide the exact expression. We finally compare our findings to numerical simulations of the fractional Brownian motion and quantify their accuracy by using the Hellinger distance.

physics.bio-ph↗

arXiv2022

Temperature and friction fluctuations inside a harmonic potential

In this article we study the trapped motion of a molecule undergoing diffusivity fluctuations inside a harmonic potential. For the same diffusing-diffusivity process, we investigate two possible interpretations. Depending on whether diffusivity fluctuations are interpreted as temperature or friction fluctuations, we show that they display drastically different statistical properties inside the harmonic potential. We compute the characteristic function of the process under both types of interpretations and analyse their limit behavior. Based on the integral representations of the processes we compute the mean-squared displacement and the normalized excess kurtosis. In the long-time limit, we show for friction fluctuations that the probability density function (PDF) always converges to a Gaussian whereas in the case of temperature fluctuations the stationary PDF can display either Gaussian distribution or generalized Laplace (Bessel) distribution depending on the ratio between diffusivity and positional correlation times.

cond-mat.stat-mech↗

arXiv2019

Diffusion-limited reactions in dynamic heterogeneous media

Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid re-arrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatio-temporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.

cond-mat.stat-mech↗

arXiv2019

Non-Gaussian diffusion of mixed origins

The properties of diffusion processes are drastically affected by heterogeneities of the medium that can induce non-Gaussian behavior of the propagator in contrast with the idealized realm of Brownian motion. In this paper we analyze the diffusion propagator when distinct origins of heterogeneity (e.g. time-fractional diffusion, diffusing diffusivity, distributed diffusivity across a population) are combined. These combinations allow one to describe new classes of strongly heterogeneous processes relevant to biology. Based on a combined subordination technique, we obtain the exact propagator for different instructive examples. This approach is then used to calculate analytically the first-passage time statistics (on half-real line and in any bounded domain) for a particle undergoing non-Gaussian diffusion of mixed origins.

cond-mat.stat-mech↗

arXiv2018

Optimal parameters for anomalous diffusion exponent estimation from noisy data

The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However, various measurement noises that are unavoidably present in experimental data, can strongly deteriorate the quality of this estimation procedure and bias the estimated exponent. To investigate the impact of noises and to improve the estimation quality, we compare three approaches for estimating the anomalous diffusion exponent and check their efficiency on fractional Brownian motion corrupted by Gaussian noise. We discuss how the parameters of this anomalous diffusion model and the parameters of the estimation techniques influence the estimated exponent. We show that the conventional linear fitting is the least optimal method for the analysis of noisy data.

physics.data-an↗

arXiv2018

A model of non-Gaussian diffusion in heterogeneous media

Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in granular media, turbulent flows, gels, and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior, and discuss some implications and extensions.

physics.bio-ph↗

arXiv2017

Statistical analysis of random trajectories of vibrated disks: towards a macroscopic realization of Brownian motion

We propose a macroscopic realization of planar Brownian motion by vertically vibrated disks. We perform a systematic statistical analysis of many random trajectories of individual disks. The distribution of increments is shown to be almost Gaussian, with slight deviations at large increments caused by inter-disk collisions. The velocity auto-correlation function takes both positive and negative values at short lag times but rapidly vanishes. We compare the empirical and theoretical distributions of time averaged mean square displacements and discuss distinctions between its mean and mode. These well-controlled experimental data can serve for validating statistical tools developed for the analysis of single-particle trajectories in microbiology.

cond-mat.stat-mech↗

arXiv2017

Mean perimeter and mean area of the convex hull over planar random walks

We investigate the geometric properties of the convex hull over $n$ successive positions of a planar random walk, with a symmetric continuous jump distribution. We derive the large $n$ asymptotic behavior of the mean perimeter. In addition, we compute the mean area for the particular case of isotropic Gaussian jumps. While the leading terms of these asymptotics are universal, the subleading (correction) terms depend on finer details of the jump distribution and describe a "finite size effect" of discrete-time jump processes, allowing one to accurately compute the mean perimeter and the mean area even for small $n$, as verified by Monte Carlo simulations. This is particularly valuable for applications dealing with discrete-time jumps processes and ranging from the statistical analysis of single-particle tracking experiments in microbiology to home range estimations in ecology.

cond-mat.stat-mech↗