Related papers: Diffusion hitting times and the Bell-shape
In this article, it is proved that for any cumulative distribution function with compact support and a specified t > 0, there exists a diffusion martingale which has this law at time t. The article proves existence; no claims are made about…
We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…
We study the variation of the mean cross section with the density of the samples in the quantum scattering of a particle by a disordered target. The target consists of a set of pointlike scatterers, each having an equal probability of being…
We propose a family of First Hitting Diffusion Models (FHDM), deep generative models that generate data with a diffusion process that terminates at a random first hitting time. This yields an extension of the standard fixed-time diffusion…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
In this article, we consider time-inhomogeneous diffusive particle systems, whose particles jump from the boundary of a bounded open subset of $\R^d$, $d\geq 1$. We give a sufficient criterion for the family of empirical distributions of…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
We study a doubly parabolic Keller-Segel system in one spatial dimension, with diffusions given by fractional laplacians. We obtain several local and global well-posedness results for the subcritical and critical cases (for the latter we…
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t)…
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes…
This article is accepted for publication in the "Annals I.H.P. Prob. & Stat.". We investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T') of the discrete setting, cf.…
We propose here a new model to describe biological invasions in the plane when a strong diffusion takes place on a line. We establish the main properties of the system, and also derive the asymptotic speed of spreading in the direction of…
We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
The Kuramoto-Sivashinsky equation with fixed boundary conditions is numerically studied. Shocklike structures appear in the time-averaged patterns for some parameter range of the boundary values. Effective diffusion constant is estimated…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and…
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…