Related papers: Convergence of symmetric trap models in the hyperc…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
Heterogeneous media diffusion is often described using position-dependent diffusion coefficients and estimated indirectly through mean squared displacement in experiments. This approach may overlook other mechanisms and their interaction…
We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with…
For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…
We study the effects of a power-law trapping potential on the scaling behaviour of the entanglement at the quantum critical point of one-dimensional (1D) lattice particle systems. We compute bipartite von Neumann and Renyi entropies in the…
The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system, but also the entropic uncertainty measures of…
We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained…
We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the…
Mean field models are a popular tool used to analyse load balancing policies. In some cases the waiting time distribution of the mean field limit has an explicit form. In other cases it can be computed as the solution of a set of…
In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation…
In this paper we use counting arguments to prove that the expected percentage coverage of a $d$ dimensional parameter space of size $n$ when performing $k$ trials with either Latin Hypercube sampling or Orthogonal sampling (when $n=p^d$) is…
We study the properties of homogeneous and isotropic turbulence in higher spatial dimensions through the lens of chaos and predictability using numerical simulations. We employ both direct numerical simulations (DNS) and numerical…
We prove the existence of a successful coupling for $n$ particles in the symmetric inclusion process. As a consequence we characterize the ergodic measures with finite moments, and obtain sufficient conditions for a measure to converge in…
We study the counterpart to the multi-photon down conversion in the quantised motion of a trapped atom. The Lamb-Dicke approximation leads to a divergence of the mean motional excitation in a finite interaction time for k-quantum down…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…
The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process takes its values in $[0,\infty)$, is ergodic and irreversible.…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
We provide a probabilistic analysis of the banker algorithm when transition probabilities may depend on time and space. The transition probabilities evolve, as time goes by, along the trajectory of an ergodic Markovian environment, whereas…