相关论文: Two Non-holonomic Lattice Walks in the Quarter Pla…

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this…

We continue the investigations of lattice walks in the three dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given length. After renormalization, this number may be interpreted as…

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…

The Half-Plane Half-Comb walk is a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e. horizontal lines below the x-axis are removed. We prove that the…

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…

We analyse a biased random walk on a 1D lattice with unequal step lengths. Such a walk was recently shown to undergo a phase transition from a state containing a single connected cluster of visited sites to one with several clusters of…

We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural random walk on a symmetric space $M$ of non-compact type and rank one. This class of spaces, which includes the complex and quaternionic…

In the past 20 years, the enumeration of plane lattice walks confined to a convex cone -- normalized into the first quadrant -- has received a lot of attention, stimulated the development of several original approaches, and led to a rich…

A method is described to count simple diagonal walks on $\mathbb{Z}^2$ with a fixed starting point and endpoint on one of the axes and a fixed winding angle around the origin. The method involves the decomposition of such walks into smaller…

The Martin boundary associated with the simple random walk on an example of partially oriented lattice is shown to be trivial by computing fine estimates of the Green kernel.

This paper concerns a random walk that moves on the integer lattice and has zero mean and a finite variance. We obtain first an asymptotic estimate of the transition probability of the walk absorbed at the origin, and then, using the…

We study the asymptotic behavior of the simple random walk on oriented version of $\mathbb{Z}^2$. The considered latticesare not directed on the vertical axis but unidirectional on the horizontal one, with symmetric random orientations…

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…

In this article we present an effective Hamiltonian approach for Discrete Time Quantum Random Walk. A form of the Hamiltonian for one dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are the generators of…

We study a natural construction of a general class of inhomogeneous quantum walks (namely walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on…

Random walks behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the…

We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove that depending on the probabilities of allowed steps, certain…

We consider the dynamical properties of Quantum Walks defined on the d-dimensional cubic lattice, or the homogeneous tree of coordination number 2d, with site dependent random phases, further characterised by transition probabilities…