Related papers: Perturbations of the Symmetric Exclusion Process
We give a characterization of the invariant measures for the exclusion process on the integers with certain reversible transition kernels. Some examples include all nearest-neighbor kernels with asymptotic mean zero. One tool used is a…
Kernels of $\alpha$-permanental processes of the form \[ v(x,y)=u(x,y)+f(y),\qquad x,y\in S, \] in which $u(x,y)$ is symmetric, and $f$ is an excessive function for the Borel right process with potential densities $u(x,y)$, are considered.…
We give sufficient conditions on the rates of two asymmetric exclusion processes such that the existence of a blocking invariant measure for the first implies the existence of such a measure for the second. The main tool is a coupling…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form $K(x-y) = \frac{|x-y|^\alpha}{\alpha}-\frac{|x-y|^\beta}{\beta}$ using recursively generated banded and…
We consider the simple exclusion process on Z x {0, 1}, that is, an ''horizontal ladder'' composed of 2 lanes, depending on 6 parameters. Particles can jump according to a lane-dependent translation-invariant nearest neighbour jump kernel,…
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
An exact mapping is established between sequence alignment, one of the most commonly used tools of computational biology, and the asymmetric exclusion process, one of the few exactly solvable models of nonequilibrium physics. The…
We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders - a generalization of the model proposed earlier [Phys. Rev. E 89, 022138 (2014)]. The defects move with…
A multi-species generalization of the asymmetric simple exclusion process (ASEP) is studied in ordered sequential and sub-lattice parallel updating schemes. In this model particles hop with their own specific probabilities to their…
In this note we study when an invariant probability measure lifts to an invariant measure. Consider a standard Borel space $X$, a Borel probability measure $\mu$ on $X$, a Borel map $T \colon X \to X$ preserving $\mu$, a compact metric…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
We study a 2-parametric family of probability measures on the space of countable point configurations on the punctured real line (the points of the random configuration are concentrated near zero). These measures (or, equivalently, point…
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
In the asymmetric simple exclusion process on the integers each particle waits exponential time, then with probability p it moves one step to the right if the site is unoccupied, otherwise it stays put; and with probability q=1-p it moves…
We study the symmetric simple exclusion process in two or higher dimensions. We prove the invariance principles for the occupation time when the process starts from nonequilibrium measures. Our proof combines the martingale method and…
It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of…