Related papers: Algebraically recurrent random walks on groups
We construct, for each real number $0\leq \alpha \leq 1$, a random walk on a finitely generated semigroup whose speed exponent is $\alpha$. We further show that the speed function of a random walk on a finitely generated semigroup can be…
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.
It is shown that the path of a simple random walk on any graph, consisting of all vertices visited and edges crossed by the walk, is almost surely a recurrent subgraph.
We introduce the notion of numerical semigroups generated by concatenation of arithmetic sequences and show that this class of numerical semigroups exhibit multiple interesting behaviours.
We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.
Wildberger gave a method to construct a finite hermitian discrete hypergroup from a random walk on a certain kind of graphs. In this article, we reveal that his method is applicable to a random walk on a certain kind of infinite graphs.…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
This paper introduces a group-theoretic framework to analyze the algebraic structure of the Grover walk on a complete graph with self-loops. We construct a group generated by the Grover matrix and a diagonal matrix whose entries are powers…
Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an…
The article provides an explicit algebraic expression for the generating function of walks on graphs. Its proof is based on the scattering theory for the differential Laplace operator on non-compact graphs.
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…
Wildberger's construction enables us to obtain a hypergroup from a special graph via random walks. We will give a probability theoretic interpretation to products on the hypergroup. The hypergroup can be identified with a commutative…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
We study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple {\em gluing} of such. In one of our simplest constructions---the {\em…
To what extent is the underlying distribution of a finitely supported unbiased random walk on $\mathbb{Z}$ determined by the sequence of times at which the walk returns to the origin? The main result of this paper is that, in various…
Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.
For any finitely generated group G, let n ---> \Phi_G(n) be the function that describes the rough asymptotic behavior of the probability of return to the identity element at time 2n of a symmetric simple random walk on G (this is an…