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The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale invariant. Abstract stochastic calculus immediately gives us…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
In this work, we analyse the metastability of non-reversible diffusion processes $$dX_t=\boldsymbol{b}(X_t)dt+\sqrt h\,dB_t$$ on a bounded domain $\Omega$ when $\mathbf{b}$ admits the decomposition $\mathbf{b}=-(\nabla f+\mathbf{\ell})$ and…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
We study the Fleming-Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
We study long time behavior of a discrete time weakly interacting particle system, and the corresponding nonlinear Markov process in $\mathbb{R}^d$, described in terms of a general stochastic evolution equation. In a setting where the state…
We study branching diffusions in a bounded domain $D$ of $\mathbb{R}^d$ in which particles are killed upon hitting the boundary $\partial D$. It is known that any such process undergoes a phase transition when the branching rate $\beta$…
The adsorption of particles diffusing in a half-space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
Heterogeneous diffusion with spatially changing diffusion coefficient arises in many experimental systems like protein dynamics in the cell cytoplasm, mobility of cajal bodies and confined hard-sphere fluids. Here, we showcase a simple…
We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the…
We investigate a method for extracting nonlinear principal components (NPCs). These NPCs maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate probability…