Related papers: Large deviations of a random walk model with emerg…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to…
We model financial transactions as random walks on activity-driven temporal networks. By enforcing fund conservation, our framework analytically derives heavy-tailed distributions for the stationary balances and transaction sizes.…
This article reviews a few basic features of systems of one-dimensional diffusions with rank-based characteristics. Such systems arise in particular in the modelling of financial markets , where they go by the name of Atlas models. We…
In this paper, we consider the problem of path finding for a set of homogeneous and autonomous agents navigating a previously unknown stochastic environment. In our problem setting, each agent attempts to maximize a given utility function…
The patterns of motion of mobile agents has received recently wide attention in the literature. There is a number of recent studies centered around the motion behavior of many agents ranging from albatrosses to human beings. Special…
Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
We study branching random walks in random i.i.d. environment in $\Z^d, d \geq 1$. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience,…
For certain natural families of topologies, we study continuity and stability of statistical properties of random walks on linear groups over local fields. We extend large deviation results known in the Archimedean case to non-Archimedean…
We study the one-dimensional branching random walk in the case when the step size distribution has a stretched exponential tail, and, in particular, no finite exponential moments. The tail of the step size $X$ decays as $\mathbb{P}[X \geq…
Scaling mobility patterns have been widely observed for animals. In this paper, we propose a deterministic walk model to understand the scaling mobility patterns, where walkers take the least-action walks on a lattice landscape and prey.…
In this work, we study the large deviation properties of random walk in a random environment on $\mathbb{Z}^d$ with $d\geq1$. We start with the quenched case, take the point of view of the particle, and prove the large deviation principle…
Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
A probabilistic approach is provided to establish new hypergeometric identities. It is based on the calculation of moments of the limiting distribution of the position of the elephant random walk in the superdiffusive regime.
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
We study sample-path large deviations for L\'evy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the $J_1$…