Related papers: Exclusion statistics and lattice random walks
Using the standard formulation of algebraic random walks (ARWs) via coalgebras, we consider ARWs for co-and Hopf-algebraic structures in the ring of symmetric functions. These derive from different types of products by dualisation, giving…
Feller's book An Introduction to Probability Theory and Its Application discusses statistics corresponding to sequences of coin tosses, with a dollar being won or lost depending on the outcome of each toss. This is equivalent to analyzing…
We consider quadrangulations with a boundary and derive explicit expressions for the generating functions of these maps with either a marked vertex at a prescribed distance from the boundary, or two boundary vertices at a prescribed mutual…
We introduce the headway exclusion process which is an exclusion process with $N$ particles on the one-dimensional discrete torus with $L$ sites with jump rates that depend only on the distance to the next particle in the direction of the…
A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate…
Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the…
We study semi-infinite 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…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
We consider a one-dimensional continuous time random walk with transition rates depending on an underlying autonomous simple symmetric exclusion process starting out of equilibrium. This model represents an example of a random walk in a…
We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The…
We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on $\mathbb Z^d$, $d\ge 2$. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has…
Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $ N $ on a two-dimensional square lattice for large $ N $, taking into account…
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
We show that Haldanes new definition of statistics, when generalised to infinite dimensional Hilbert spaces, is equal to the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter, g ,…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We…
A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…