Related papers: Some Combinatorial Identities from the Random Walk
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…
The vicious random walker problem on a one dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site are prohibited. It is known that the…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of which two special cases are already known in literature.
We consider a class of self-interacting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the d-dimensional integer lattice. The main purpose of this paper is two-fold: to give a survey…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
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…
Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We prove that the combinatorics generated by the quantum random walk on Z can be interpreted from the reading of periodic orbits of the classical chaotic map $x \mapsto 2x mod 1$.
A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of…
We investigate a space-inhomogeneous discrete-time quantum walk in one dimension. We show that the walk exhibits localization by a path counting method.
We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label…
Recently, Andrews and Yee studied two-variable generalizations of two identities involving partition functions $p_\omega(n)$ and $p_\nu(n)$ introduced by Andrews, Dixit and Yee. In this paper, we present a combinatorial proof of an…
A new class of one-dimensional, discrete time random walk model with memory, termed "Random walk with $n$ memory channels" (RW$n$MC) is proposed. In this model the information of $n$ ($n\in \mathbb{Z}$) previous steps from the walker's…
In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new…
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…
A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or…
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…