arXiv subjects

M. Dolgushev

Publications and source records attributed to M. Dolgushev.

6 recordsLinked to original sources

arXiv2025

Evidence and quantification of memory effects in competitive first passage events

Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian) processes. However, in complex systems such as polymer fluids, the motion of a particle should typically be described as a process with memory, for which splitting probabilities are much less characterized analytically. Here, we introduce an analytical approach that provides the splitting probabilities for one-dimensional isotropic non-Markovian Gaussian processes with stationary increments, in the case of two targets. This analysis shows that splitting probabilities are controlled by the out of equilibrium trajectories observed after the first passage. This is directly evidenced in a prototypical experimental reaction scheme in viscoelastic fluids. These results are extended to $d$-dimensional processes in large confining volumes, opening a path towards the study of competitive events in complex media.

cond-mat.stat-mech↗

arXiv2024

Visitation Dynamics of $d$-Dimensional Fractional Brownian Motion

The fractional Brownian motion (fBm) is a paradigmatic strongly non-Markovian process with broad applications in various fields. Despite their importance, the properties of the territory covered by a $d$-dimensional fBm have remained elusive so far. Here, we study the visitation dynamics of the fBm by considering the time $τ_n$ required to visit a site, defined as a unit cell of a $d$-dimensional lattice, when $n$ sites have been visited. Relying on scaling arguments, we determine all temporal regimes of the probability distribution function of $τ_n$. These results are confirmed by extensive numerical simulations that employ large-deviation Monte Carlo algorithms. Besides these theoretical aspects, our results account for the tracking data of telomeres in the nucleus of mammalian cells, microspheres in an agorose gel, and vacuoles in the amoeba, which are experimental realizations of fBm.

cond-mat.stat-mech↗

arXiv2024

From Maximum of Intervisit Times to Starving Random Walks

Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time $τ_k$ required for a random walk to find a site that it never visited previously, when the walk has already visited $k$ distinct sites. Here, we tackle the natural issue of the statistics of $M_n$, the longest duration out of $τ_0,\dots,τ_{n-1}$. This problem belongs to the active field of extreme value statistics, with the difficulty that the random variables $τ_k$ are both correlated and non-identically distributed. Beyond this fundamental aspect, we show that the asymptotic determination of the statistics of $M_n$ finds explicit applications in foraging theory and allows us to solve the open $d$-dimensional starving random walk problem, in which each site of a lattice initially contains one food unit, consumed upon visit by the random walker, which can travel $\mathcal{S}$ steps without food before starving. Processes of diverse nature, including regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, share common properties within the same universality classes.

cond-mat.stat-mech↗

arXiv2023

Imperfect Narrow Escape problem

We consider the kinetics of the imperfect narrow escape problem, i.e. the time it takes for a particle diffusing in a confined medium of generic shape to reach and to be adsorbed by a small, imperfectly reactive patch embedded in the boundary of the domain, in two or three dimensions. Imperfect reactivity is modeled by an intrinsic surface reactivity $κ$ of the patch, giving rise to Robin boundary conditions. We present a formalism to calculate the exact asymptotics of the mean reaction time in the limit of large volume of the confining domain. We obtain exact explicit results in the two limits of large and small reactivities of the reactive patch, and a semi-analytical expression in the general case. Our approach reveals an anomalous scaling of the mean reaction time as the inverse square root of the reactivity in the large reactivity limit, valid for an initial position near the extremity of the reactive patch. We compare our exact results with those obtained within the ``constant flux approximation''; we show that this approximation turns out to give exactly the next-to-leading order term of the small reactivity limit, and provides a good approximation of the reaction time far from the reactive patch for all reactivities, but not in the vicinity of the boundary of the reactive patch due to the above mentioned anomalous scaling. These results thus provide a general framework to quantify the mean reaction times for the imperfect narrow escape problem.

cond-mat.stat-mech↗

arXiv2022

Marginally compact hyperbranched polymer trees

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution or the shear-stress relaxation modulus, are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass $N$, this effect becomes rapidly irrelevant with increasing spacer length $S$. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time $τ_p$ of mode $p$ must scale as $τ_p \sim (N/p)^{5/3}$ rather than the usual square power law for linear chains.

cond-mat.soft↗

arXiv2019

Survival probability of stochastic processes beyond persistence exponents

For many stochastic processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\sim S_0/t^θ$. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent $θ$ has been studied at length, the prefactor $S_0$, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for $S_0$ for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for $S_0$ are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.

cond-mat.stat-mech↗