Related papers: Short-time Gibbsianness for Infinite-dimensional D…
We consider the Gibbs-measures of continuous-valued height configurations on the $d$-dimensional integer lattice in the presence a weakly disordered potential. The potential is composed of Gaussians having random location and random depth;…
By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite dimensional Hilbert space. We compare our general expressions with numerical…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…
We focus on the log-Sobolev inequality for spin systems on the lattice with interactions of higher order than quadratic. We show that if the one-dimensional single-site measure with boundaries satisfies the log-Sobolev inequality uniformly…
We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-\alpha}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse…
This paper studies the large time behavior of aggregation-diffusion equations. For one spatial dimension with certain assumptions on the interaction potential, the diffusion index $m$, and the initial data, we prove the convergence to the…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a…
Consider a sequence of Gibbsian line ensembles, whose lowest labeled curves (i.e., the edge) have tight one-point marginals. Then, given certain technical assumptions on the nature of the Gibbs property and underlying random walk measure,…
This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the…
In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However,…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
The distribution $g_{cl}$ of a Gibbs cluster point process in $X=\mathbb{R}^{d}$ (with i.i.d. random clusters attached to points of a Gibbs configuration with distribution $g$) is studied via the projection of an auxiliary Gibbs measure…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
A theory of intermittency differentiation is developed for a general class of 1D Infinitely Divisible Multiplicative Chaos measures. The intermittency invariance of the underlying infinitely divisible field is established and utilized to…