Related papers: Self-avoiding walks and polygons confined to a squ…

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area,…

Motivated by the problem of finding resistances among vertices in a hypercube, we derive exact expressions, generating functions, and asymptotic expansions for these resistances, then study the combinatorial interpretations of the…

We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical - the discrete-time Polya walk, in which the walker steps at each integer moment of time, and…

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…

Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some…

We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifolds. Asymptotic behavior of end invariants in a convergent…

For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations.…

We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…

Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in $n$-dimensional Euclidean space bounded by hyperplanes), thus solving problems posed by Grabiner [J. Combin. Theory…

In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given…

In the present paper, we study long time asymptotics of non-symmetric random walks on crystal lattices from a view point of discrete geometric analysis due to Kotani and Sunada [11, 23]. We observe that the Euclidean metric associated with…

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…

Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that…

Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly related to other discrete structures. While walks restricted to…

We study the asymptotic behaviour of 1-parameter subgroups with respect to Hofer's metric when the underlying symplectic manifold is an open surface of infinite area. We prove that, depending on the topology of the level sets of the…

We have extended the enumeration of self-avoiding walks on the Manhattan lattice from 28 to 53 steps and for self-avoiding polygons from 48 to 84 steps. Analysis of this data suggests that the walk generating function exponent gamma =…

In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an…

We consider the sum of the coordinates of a simple random walk on the K-dimensional hypercube, and prove a double asymptotic of this process, as both the time parameter n and the space parameter K tend to infinity. Depending on the…

We use the lattice model of directed walks to investigate the conformational as well as the adsorption properties of a semiflexible homopolymer chain immersed in a good solvent in two and three dimensions. To account for the stiffness in…

Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an…