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The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Stochastic restart may drastically reduce the expected run time of a computer algorithm, expedite the completion of a complex search process, or increase the turnover rate of an enzymatic reaction. These diverse first-passage-time (FPT)…
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…
We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…
In this paper a general theorem of constructing infinite particle systems of jump types with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction…
We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are…
Several families of one-point interactions are derived from the system consisting of two and three $\delta$-potentials which are regularized by piecewise constant functions. In physical terms such an approximating system represents two or…
A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given…
The kinetics of irreversible annihilation of charged particles performing overdamped motion induced by long-range interaction force, $F(r)\sim r^{-\lambda}$, is investigated. The system exhibits rich kinetic behaviors depending on the force…
Reversibility is a key property of Markov chains, central to algorithms such as Metropolis-Hastings and other MCMC methods. Yet many applications yield non-reversible chains, motivating the problem of approximating them by reversible ones…
We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…
We study one-dimensional hardcore lattice gases, with nearest-neighbor interactions, in the presence of an external potential barrier, that moves on the periodic lattice with a constant speed. We investigate how the nature of the…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
We consider spin systems on $\Z$ (i.e.\ interacting particle systems on $\Z$ in which each coordinate only has two possible values and only one coordinate changes in each transition) whose rates are determined by another process, called a…
We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free…
The present paper is devoted to the study of a simple model of interacting electrons in a random background. In a large interval $\Lambda$, we consider $n$ one dimensional particles whose evolution is driven by the Luttinger-Sy model, i.e.,…
We construct an additional independent integral of motion for a class of three dimensional minimally superintegrable systems with constant magnetic field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages]…
The paper examines a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential. We show that when the repulsion between particles is very large the system can be approached…