Related papers: Perturbations of the Symmetric Exclusion Process

We study the integro-differential operators $L$ with kernels $K(y) = a(y) J(y)$, where $J(y)dy$ is a L\'evy measure on $\bR^d$ (i.e. $\int_{\bR^d}(1\wedge |y|^2)J(y)dy<\infty$) and $a(y)$ is an only measurable function with positive lower…

The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes…

There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and…

Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…

We investigate properties of non-translation-invariant measures, describing particle systems on $\bbz$, which are asymptotic to different translation invariant measures on the left and on the right. Often the structure of the transition…

For polynomial $ P (x,y)$, and any Calder\'{o}n-Zygmund kernel, $K$, the operator below satisfies a $ (1,r)$ sparse bound, for $ 1< r \leq 2$. $$ \sup _{\epsilon >0} \Bigl\lvert \int_{|y| > \epsilon} f (x-y) e ^{2 \pi i P (x,y) } K(y) \; dy…

Model checking is the process of deciding whether a system satisfies a given specification. Often, when the setting comprises multiple processes, the specifications are over sets of input and output signals that correspond to individual…

We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned, in several settings. (i) We consider a regression task, where the target function is a Gaussian random field that depends…

We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…

We investigate the correlation functions of the one-dimensional Asymmetric Simple Exclusion Process (ASEP) with open boundaries. The conditions for the boundaries are made most general. The correlation function is expressed in a multifold…

We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an environment. For each environment p we prove that the set of all invariant measures is the convex hull of a set of…

In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations.…

Multi-particle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three non-equilibrium…

Let $X$ and $Y$ be two independent identically distributed random variables with density $p(x)$ and $Z=\alpha X+\beta Y$ for some constants $\alpha>0$ and $\beta>0$. We consider the problem of estimating $p(x)$ by means of the samples from…

The effect of a moving defect particle for the one-dimensional partially asymmetric simple exclusion process on a ring is considered. The current of the ordinary particles, the speed of the defect particle and the density profile of the…

Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance…

In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…

We give a combinatorial description of the stationary measure for a totally asymmetric exclusion process (TASEP) with second class particles, on either Z or on the cycle Z_N. The measure is the image by a simple operation of the uniform…

We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to…

In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability measure for each p.