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We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching…
Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
We study systems of interacting Brownian particles in one dimension constructed as the diffusion scaling limits of Fisher's vicious walk models. We define two types of nonintersecting Brownian motions, in which we impose no condition (resp.…
We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
We derive asymptotic formulas for the mean exit time $\bar{\tau}^{N}$ of the fastest among $N$ identical independently distributed Brownian particles to an absorbing boundary for various initial distributions (partially uniformly and…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…
Understanding the out-of-equilibrium properties of noisy microscale systems and the extent to which they can be modulated externally, is a crucial scientific and technological challenge. It holds the promise to unlock disruptive new…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\alpha$,…
We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{\alpha-1}$, $\alpha>0$ (scaled Brownian motion), is stochastically reset to its initial position and…
We analyze the escape of Brownian particles over potential barriers using the Fokker-Planck equation in a similar way to that of Chandrasekhar (Rev. Modern Phys., 1943), deriving a formula for the particle deposition velocity to a surface…
Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times…
We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key…
Systems comprised of self-steering active Brownian particles are studied via simulations for a minimal cognitive flocking model. The dynamics of the active Brownian particles is extended by an orientational response with limited…