Related papers: Grover Walks on a Line with Absorbing Boundaries

We consider the Grover walk on infinite trees from the view point of spectral analysis. From the previous works, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this…

The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal…

We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom…

A complete representation of the Martin boundary of killed random walks on a half-space $\Z^{d-1}\times\N^*$ is obtained. In particular, it is proved that the corresponding Martin boundary is homemorphic to the half-sphere ${\cal S}^d_+ =…

We give exact and explicit expressions of mean first-passage times for random walks in a rectangular domain, in both cases of reflecting boundary conditions and periodic boundary conditions. The situations with one or two absorbing targets…

This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.

A notion of up and down Grover walks on simplicial complexes are proposed and their properties are investigated. These are abstract Szegedy walks, which is a special kind of unitary operators on a Hilbert space. The operators introduced in…

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…

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…

Concerning a discrete-time quantum walk X^{(d)}_t with a symmetric distribution on the line, whose evolution is described by the Hadamard transformation, it was proved by the author that the following weak limit theorem holds: X^{(d)}_t /t…

The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or…

We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to…

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…

We show that the expected time for a random walk on a (multi-)graph $G$ to traverse all $m$ edges of $G$, and return to its starting point, is at most $2m^2$; if each edge must be traversed in both directions, the bound is $3m^2$. Both…

As soon as Lyman or Balmer lines overlap, the net absorption cross section rapidly approaches the value at the series limit. Independent of the difficult question of the relative contributions of line and continuous opacity, we can get a…

Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by $7^{th}$-order time-series expansion are successfully compared. The…

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…

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…

While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a…