Related papers: Smooth Paths on Three Dimensional Lattice

We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…

Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite…

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…

Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…

In spin-lattice models with order parameter conserved, we generalize the idea of spin diffusion incorporating a variety factors as possible driving forces, including the external field and the temperature. The Kawasaki dynamics in the…

Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a…

A three dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices,…

In this work we investigate the critical behavior of the three dimensional simple-cubic Majority voter model. Using numerical simulations and a combination of two different cumulants we evaluated the critical point with a higher accuracy…

Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…

We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…

Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…

We consider a supercritical symmetric continuous-time branching random walk on a multidimensional lattice with a finite number of particle generation sources of varying positive intensities without any restrictions on the variance of jumps…

In this article, we consider the number of collisions of three independent simple random walks on a subgraph of the two-dimensional square lattice obtained by removing all horizontal edges with vertical coordinate not equal to 0 and then,…

We answer some questions on the asymptotics of ballot walks raised in [Personal Journal Shalosh B Ekhad and Doron Zeilberger, Apr 5, 2021; see also arXiv:2104.01731] and prove that these models are not D-finite. This short note demonstrates…

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which…

Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…

Quantum random walks, - coined, lattice ones, - exhibit ballistic behavior with fascinating asymptotic patterns of the amplitudes. We show that averaging over the coins (using the Haar measure), these patterns blend into a spline. Also, we…