Related papers: Infinite variance $H$-sssi processes as limits of …
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
Let $\Delta\subsetneq\V$ be a proper subset of the vertices $\V$ of the defining graph of an irreducible and aperiodic shift of finite type $(\Sigma_{A}^{+},\S)$. Let $\Sigma_{\Delta}$ be the subshift of allowable paths in the graph of…
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence that can have long-range dependence. In this paper, we find the scaling limit of a random walk that follows GBP. The result is a new class of…
In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
We study the local asymptotics at the edge for particle systems arising from: (i) eigenvalues of sums of unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions of tensor products of representations…
We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…
An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
Combinatorial Levy processes evolve on general state spaces of countable combinatorial structures. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the…
We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
The continuous-time random walk is defined as a Poissonization of discrete-time random walk. We study the noncolliding system of continuous-time simple and symmetric random walks on ${\mathbb{Z}}$. We show that the system is determinantal…
According to Pruessner and Peters [Phys. Rev. E {\bf 73}, 025106(R) (2006)], the finite size scaling exponents of the order parameter in sandpile models depend on the tuning of driving and dissipation rates with system size. We point out…
In this article we study limits of models that contain a dimensionful parameter such as the mass of the relativistic point-particle. The limits are analogous to the massless limit of the particle and may be thought of as high energy limits.…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
For several classes of bounded sets $A$, the limit of a one-dimensional L\'{e}vy process conditioned to avoid $A$ up to a parametrized random time which tends to infinity. For $A$ we take the set of finite points with several clocks and a…