相关论文: On the Ergodicity of Interacting Particle Systems …
We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an $L^1$ transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of…
The Dirichlet forms related to various infinite systems of interacting Brownian motions are studied. For a given random point field $ \mu $, there exist two natural infinite-volume Dirichlet forms $…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
We present a thermodynamic description of ultracold gases with dipolar interactions which properly accounts for the long-range nature and broken rotation invariance of the interactions. It involves an additional thermodynamic field…
We study the regularity of a diffusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and reflection between nearest neighbors. As our…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension $d\ge 2$. The process is associated with the Dirichlet form defined by integration of the…
This paper deals with some self-interacting diffusions $(X_t,t\geq 0)$ living on $\mathbb{R}^d$. These diffusions are solutions to stochastic differential equations: \[\mathrm{d}X_t=\mathrm{d}B_t-g(t)\nabla…
Aims. The random walk of energetic charged particles in turbulent magnetic fields is investigated. Special focus is placed on transport across the mean magnetic field, which had been found to be subdiffusive on many occasions. Therefore, a…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
We study equilibrium states of an infinite system of interacting particles in a Euclidean space. The particles bear `unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is pairwise and splits…
We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized…
We consider Markov processes that alternate continuous motions and jumps in a general locally compact polish space. Starting from a mechanistic construction, a first contribution of this article is to provide conditions on the dynamics so…
In this paper we study the Poisson process over a $\sigma$-finite measure-space equipped with a measure preserving transformation or a group of measure preserving transformations. For a measure-preserving transformation $T$ acting on a…
We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of…
We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity…