Related papers: Automatic Classification of Restricted Lattice Wal…
We recently published [J. Phys A: Math. Theor. {\bf 45} 115202 (2012)] a new and more efficient implementation of a transfer-matrix algorithm for exact enumerations of self-avoiding polygons. Here we extend this work to the enumeration of…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
In the past decade, a lot of attention has been devoted to the enumera-tion of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear…
The problem of missing link prediction in complex networks has attracted much attention recently. Two difficulties in link prediction are the sparsity and huge size of the target networks. Therefore, the design of an efficient and effective…
In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems.…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
We study the path behaviour of a simple random walk on the 2-dimensional comb lattice ${\mathbb C}^2$ that is obtained from ${\mathbb Z}^2$ by removing all horizontal edges off the x-axis. In particular, we prove a strong approximation…
This work is devoted to the analysis of a Gibbs partition model, also known as a composition scheme. We consider a natural new condition on the component weights. It leads to a new behavior for the total number of components. We discover a…
Initial steps are presented towards understanding which finitely generated groups are almost surely generated as semigroups by the path of a random walk on the group.
In random walk theory, it is customary to assume that a given walk is irreducible and/or aperiodic. While these prevailing assumptions make particularly tractable the analysis of random walks and help to highlight their diffusive nature,…
We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in…
We propose a novel combinatorial algorithm for efficient generation of Hamiltonian walks and cycles on a cubic lattice, modeling the conformations of lattice toy proteins. Through extensive tests on small lattices (allowing complete…
A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…
We obtain expected number of arrivals, absorption probabilities and expected time before absorption for a discrete random walk on the integers with an infinite set of equidistant multiple function barriers
We count the number of closed walks on a vertex in a regular tree using the Catalan's triangle and also the Borel's triangle, showing another combinatorial structure counted by these two array of numbers.
Lattice QCD allows computations of moments of structure functions from first principles. An overview of the present status of the calculations is given. Recent results and future perspectives are discussed.
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…