Related papers: Cooling gases with Levy flights: using the general…
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…
The semiclassical theory of laser cooling is applied for the analysis of cooling of unbound atoms with the values of the ground and exited state angular moments 1/2 in a one-dimensional nondissipative optical lattice. We show that in the…
This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps,…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We consider the combined effects of a power law L\'{e}vy step distribution characterized by the step index $f$ and a power law waiting time distribution characterized by the time index $g$ on the long time behavior of a random walker. The…
We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of…
We prove log-concavity of the lengths of the top rows of Young diagrams under Poissonized Plancherel measure. This is the first known positive result towards a 2008 conjecture of Chen that the length of the top row of a Young diagram under…
For both Levy flight and Levy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given…
We argue that the so called long flying component (LFC) observed in some cosmic ray experiments are yet another manifestation of L\'evy distributions (with index $q=1.3$), this time of the distribution observation probability of the depths…
We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
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…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
Exact results for the first passage time and leapover statistics of symmetric and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are shown to have leapover lengths, that are asymptotically power-law distributed with…
We study a statistical mechanical model for the dynamics of lung inflation which incorporates recent experimental observations on the opening of individual airways by a cascade or avalanche mechanism. Using an exact mapping of the avalanche…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…
We study the statistics of encounters of L\'evy flights by introducing the concept of vicious L\'evy flights - distinct groups of walkers performing independent L\'evy flights with the process terminating upon the first encounter between…
The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the…