Related papers: Enumeration of simple random walks and tridiagonal…

Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta-analysis (NMA) is an active area of research. We extend this to the contributions of paths to NMA estimates. We present a general…

We give a summary of recent progress on the signed area enumeration of closed walks on planar lattices. Several connections are made with quantum mechanics and statistical mechanics. Explicit combinatorial formulae are proposed which rely…

Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

Random walks in cones have the double interest of being at the heart of many probabilistic problems and of being related to many mathematical fields, such as spectral theory, combinatorics, or discrete complex analysis. In this article, we…

Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is…

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…

Below is a method for relating a mixed volume computation for polytopes sharing many facet directions to a symmetric random walk. The example of permutahedra and particularly hypersimplices is expanded upon.

In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…

We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks,…

We prove for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n has the order of square root of n. Moment or symmetry assumptions are not necessary. In removing…

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…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

The random walk to be considered takes place in the d- spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation d of U(n). The transition matrix comes from the three term recursion relation satisfied…

Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…

We report an efficient methodology for enumerating the Hamiltonian walks in two and three dimensional lattices of large sizes, using the concept of centroids. This strategy, with the help of JAVA programming enables the exact computation of…

We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…

We address the enumeration of walks with small steps confined to a two-dimensional cone, for example the quarter plane, three-quarter plane or the slit plane. In the quarter plane case, the solutions for unweighted step-sets are already…

We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…