Related papers: Asymptotics of the Tacnode process: a transition b…

In this paper, we study the gap probability problem of the (symmetric) Jacobi unitary ensemble of Hermitian random matrices, namely the probability that the interval $(-a,a)\:(0<a<1)$ is free of eigenvalues. Using the ladder operator…

Given an autoregressive process X of order p (i.e. X_n = a_1 X_{n-1} + ...+ a_p X_{n_p} + Y_n where the random variables Y_1, Y_2, ... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a…

We consider a type of random processes which satisfies the conditional increment condition and obtain an estimate for the tail probability and a Doob-type inequality of the maximum of the process. The main result is that, for processes…

We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…

The time-integrated current of the TASEP has non-Gaussian fluctuations of order $t^{1/3}$. The recently discovered connection to random matrices and the Painlev\'e II Riemann-Hilbert problem provides a technique through which we obtain the…

Branching processes in a random environment are natural generalisations of Galton-Watson processes. In this paper we analyse the asymptotic decay of the survival probability for a sequence of slightly supercritical branching processes in an…

The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multi-species version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a finite interval. An open problem from a…

The paper presents two results. The first one provides separate conditions for the upper and lower estimate of the distribution of the exit time from balls of a random walk on a weighted graph. The main result of the paper is that the lower…

We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic…

We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…

Putting dynamics into random matrix models leads to finitely many nonintersecting Brownian motions on the real line for the eigenvalues, as was discovered by Dyson. Applying scaling limits to the random matrix models, combined with Dyson's…

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class…

A new series expansion for the the Airy function is presented here that stems from the method of steepest descents and can be related to the Hadamard expansions as presented in prevous works cited in the manuscript, and which is convergent…

In the totally asymmetric simple exclusion process (TASEP) two processes arise in the large time limit: the Airy_1 and Airy_2 processes. The Airy_2 process is an universal limit process occurring also in other models: in a stochastic growth…

The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled…

In this paper we determine bounds and exact asymptotics of the ruin probability for risk process with arrivals given by a linear marked Hawkes process. We consider the light-tailed and heavy-tailed case of the claim sizes. Main technique is…

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $ N \times N $ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…