Related papers: Heavy-tailed random walks, buffered queues and hid…
Consider the continuous greedy paths model: given a $d$-dimensional Poisson point process with positive marks interpreted as masses, let $\mathrm P(\ell)$ denote the maximum mass gathered by a path of length $\ell$ starting from the origin.…
A Lindley process arises from classical studies in queueing theory and it usually reflects waiting times of customers in single server models. In this note we study recurrence of its higher dimensional counterpart under some mild…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of…
Consider a random walk in a time-dependent random environment on the lattice Zd. Recently, Rassoul-Agha, Seppalainen and Yilmaz [RSY11] proved a general large deviation principle under mild ergodicity assumptions on the random environment…
We provide large deviations estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails with index $-\alpha, \alpha \in (1,2)$. We show that upper tail…
We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time…
We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
We study an agent-based model of animals marking their territory and evading adversarial territory in one dimension, with respect to the distribution of the size of the resulting territories. In particular, we use sophisticated sampling…
The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied.…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
In this article, we consider a branching random walk on the real-line where displacements coming from the same parent have jointly regularly varying tails. The genealogical structure is assumed to be a supercritical Galton-Watson tree,…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk repeats one of its preceding steps chosen uniformly at…
Consider a queueing system fed by traffic from $N$ independent and identically distributed marked point processes. We establish several novel sample path large deviations results in the scaled uniform topology for such a system with a small…
In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload…
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)…