English
Related papers

Related papers: First-Hitting Location Laws as Boundary Observable…

200 papers

Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…

Statistical Mechanics · Physics 2025-08-15 Daniel Marris , Chittaranjan Hens , Subrata Ghosh , Luca Giuggioli

We study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time…

Statistical Mechanics · Physics 2026-03-25 Ivan N. Burenev

We derive the asymptotic first passage time (FPT) distribution for space-dependent variable-order time-fractional diffusion, where the fractional exponent $\alpha(x)$ varies with position. For any sufficiently smooth $\alpha(x)$ on a finite…

Statistical Mechanics · Physics 2026-04-16 Wancheng Li , Daniel S. Han

A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given…

Statistical Mechanics · Physics 2025-07-15 Denis S. Grebenkov , Ralf Metzler , Gleb Oshanin

Recent large deviation results have provided general lower bounds for the fluctuations of time-integrated currents in the steady state of stochastic systems. A corollary are so-called thermodynamic uncertainty relations connecting precision…

Statistical Mechanics · Physics 2017-03-29 Juan P. Garrahan

For both Levy flight and Levy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given…

Statistical Mechanics · Physics 2019-10-15 V. V. Palyulin , G. Blackburn , M. A. Lomholt , N. W. Watkins , R. Metzler , R. Klages , A. V. Chechkin

The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of…

Subcellular Processes · Quantitative Biology 2018-12-05 Denis S. Grebenkov , Ralf Metzler , Gleb Oshanin

The mean first passage time, one of the important characteristics for a stochastic process, is often calculated assuming the observation time is infinite. However, in practice, the observation time, T, is always finite and the mean first…

Statistical Mechanics · Physics 2020-04-22 Ji-Hyun Kim , Hunki Lee , Sanggeun Song , Hye Ran Koh , Jaeyoung Sung

Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct…

Biological Physics · Physics 2017-10-02 Yiwei Li , Osman Kahraman , Christoph A. Haselwandter

A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards-Wilkinson equation with non-conserved noise and the Mullins-Herring equation with conserved noise. The profile is subject to either…

Statistical Mechanics · Physics 2018-03-28 Markus Gross

We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…

Analysis of PDEs · Mathematics 2026-02-11 Luan Hoang , Akif Ibragimov

We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…

Statistical Mechanics · Physics 2014-11-20 T. Becker , K. Nelissen , B. Cleuren , B. Partoens , C. Van den Broeck

The first-passage time (FPT) of a stochastic signal to a threshold is a fundamental observable across physics, biology, and finance. While renewal shot noise is a canonical model for such signals, analytical results for its FPT have…

Statistical Mechanics · Physics 2026-02-24 Julien Brémont

Using scaling arguments and extensive numerical simulations, we study dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall…

Statistical Mechanics · Physics 2023-07-19 A. Valov , V. Avetisov , S. Nechaev , G. Oshanin

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described…

Soft Condensed Matter · Physics 2009-11-07 Chi-Lun Lee , George Stell , Jin Wang

Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…

Statistical Mechanics · Physics 2016-08-03 Keiji Saito , Abhishek Dhar

The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a…

Probability · Mathematics 2021-03-16 Sean D Lawley

Diffusion/score-based models have emerged as powerful generative models, capable of generating high-quality samples that mimic the training data distribution. However, it has been observed that they are prone to reproducing training…

Machine Learning · Statistics 2026-05-26 Benjamin Sterling , Mónica F. Bugallo , Tom Tirer

The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…

Analysis of PDEs · Mathematics 2016-11-03 Martin Burger , Jan-Frederik Pietschmann

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…

Statistical Mechanics · Physics 2019-01-30 V. Sposini , A. V. Chechkin , R. Metzler