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The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
We propose a Monte Carlo method which performs a random walk in energy space using cluster-like collective updates. By imposing that bond probabilities depend continuously on the microcanonical temperature, we obtain dynamic exponents close…
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
We study a random walk in random environment on the non-negative integers. The random environment is not homogeneous in law, but is a mixture of two kinds of site, one in asymptotically vanishing proportion. The two kinds of site are (i)…
In any valid Monte Carlo sampling that realizes microcanonical property we can collect statistics for a transition matrix in energy. This matrix is used to determine the density of states, from which most of the thermodynamical averages can…
Random walks on the circle group $\mathbb{R}/\mathbb{Z}$ whose elementary steps are lattice variables with span $\alpha \not\in \mathbb{Q}$ or $p/q \in \mathbb{Q}$ taken mod $\mathbb{Z}$ exhibit delicate behavior. In the rational case we…
A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation…
The quantum XXZ spin-1/2 chain features non-Gaussian spin current fluctuations in the regime of easy-axis anisotropy. Using ballistic macroscopic fluctuation theory, we derive the exact probability distribution of typical spin-current…
We analytically investigate the one-excitation spin dynamics in a homogeneous closed spin-1/2 chain via diagonalization of the one-excitation block of the XX-Hamiltonian, which allows to derive the analytical expressions for probability…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
The phenomenon of macroscopic homogenization is illustrated with a simple example of diffusion. We examine the conditions under which a $d$--dimensional simple random walk in a symmetric random media converges to a Brownian motion. For…
A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard $n$-dimensional…
We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.
Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of…
The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ)…