Related papers: Infinite-Scale Percolation in a New Type of Branch…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…
In this letter we describe a new micro-bunching instability occurring in charged particle beams propagating along a straight trajectory: based on the dynamics we named it a Plasma Cascade Instability.
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
We study a supposed model for branched polymers which was shown in two dimensions to be in the universality class of ordinary percolation. We confirm this by high statistics simulations and show that it is in the percolation universality…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
A two-type continuous-state branching process in varying environments is constructed as the pathwise unique solution of a system of stochastic equations driven by time-space noises, where the pathwise uniqueness is derived from a comparison…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
A general class of non-Markov, supercritical Gaussian branching particle systems is introduced and its long-time asymptotics is studied. Both weak and strong laws of large numbers are developed with the limit object being characterized in…
Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an $O(1)$-window) for…
In this paper we present theory of novel micro-bunching instability. We named it Plasma-Cascade Instability
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
We propose a stochastic branching particle-based method for solving nonlinear non-conservative advection-diffusion-reaction equations. The method splits the evolution into an advection-diffusion step, based on a linearized Kolmogorov…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…