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Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…

Probability · Mathematics 2013-09-11 Alexander Drewitz , Alejandro F. Ramírez

The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…

Numerical Analysis · Mathematics 2007-05-23 Tony Lelievre , Mohamed El Makrini , Benjamin Jourdain

We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law…

Statistical Mechanics · Physics 2009-11-13 L. Padilla , H. O. Mártin , J. L. Iguain

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two…

Statistical Mechanics · Physics 2009-10-02 Ingo Lohmar , Joachim Krug

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…

Probability · Mathematics 2019-12-12 Samuel Herrmann , Nicolas Massin

We present dielectric spectroscopy data obtained for gallium-doped Cd$_{0.99}$Mn$_{0.01}$Te:Ga mixed crystals which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1.…

Statistical Mechanics · Physics 2011-11-15 Justyna Trzmiel , Karina Weron , Aleksander Stanislavsky , Agnieszka Jurlewicz

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…

Classical Analysis and ODEs · Mathematics 2007-05-23 Sabir Umarov , Stanly Steinberg

We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum…

Statistical Mechanics · Physics 2015-05-27 H. V. Ribeiro , E. K. Lenzi , R. S. Mendes , P. A. Santoro

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem…

Statistical Mechanics · Physics 2007-05-23 L. Acedo , S. B. Yuste

A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate…

Statistical Mechanics · Physics 2009-10-28 John Cardy , Uwe C. Täuber

We consider a random walk on the support of an ergodic simple point process on R^d, d>1, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a…

Mathematical Physics · Physics 2007-05-23 A. Faggionato , P. Mathieu

Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…

Probability · Mathematics 2023-06-05 Ryuya Namba

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance…

Probability · Mathematics 2007-05-23 F. Rassoul-Agha , T. Seppalainen

We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d \ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit…

Probability · Mathematics 2007-12-06 Nobuo Yoshida

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper…

Mathematical Physics · Physics 2015-05-27 Z. Haba

We use a recently-derived reformulation of the diffusion constant [Stillinger F H and Debenedetti P G 2005 J. Phys. Chem. B 109 6604] to investigate heterogeneous dynamics and non-Gaussian diffusion in a binary Lennard-Jones mixture. Our…

Soft Condensed Matter · Physics 2007-05-23 M. Scott Shell , Pablo G. Debenedetti , Frank H. Stillinger

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Optimization and Control · Mathematics 2019-03-15 Melike Sirlanci , Susan E. Luczak , I. Gary Rosen

We consider the phase coherent transport of a quasi one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow identified in [T. Paul et al., Phys. Rev.…

Quantum Gases · Physics 2009-09-18 T. Paul , M. Albert , P. Schlagheck , P. Leboeuf , N. Pavloff

We derive a renormalization method to calculate the spectral dimension $\bar{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of…

Statistical Mechanics · Physics 2015-05-13 Christophe P. Haynes , Anthony P. Roberts

We consider the penetration length $l$ of random walkers diffusing in a medium of perfect or imperfect absorbers of number density $\rho$. We solve this problem on a lattice and in the continuum in all dimensions $D$, by means of a…

Statistical Mechanics · Physics 2009-11-11 David S. Dean , Clément Sire , Julien Sopik