Related papers: D\'eviations mod\'er\'ees de la distance chimique
The asymptotic distance between trajectories $d_{\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a…
We derive the moderate deviation principles for the fluctuation fields of the facilitated exclusion process (FEP) in one dimension when the process starts from its stationary measure, both in the symmetric and asymmetric cases. The main…
A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown…
We consider random walk and self-avoiding walk whose 1-step distribution is given by $D$, and oriented percolation whose bond-occupation probability is proportional to $D$. Suppose that $D(x)$ decays as $|x|^{-d-\alpha}$ with $\alpha>0$.…
We study the long range percolation model on $\mathbb{Z}$ where sites $i$ and $j$ are connected with probability $\beta |i-j|^{-s}$. Graph distances are now well understood for all exponents $s$ except in the case $s=2$ where the model…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it…
We study translation-invariant determinantal random point fields on the real line. We prove, under quite general conditions, that the smallest nearest spacings between the particles in a large interval have Poisson statistics as the length…
Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
We present high statistics data on the distribution of shortest path lengths between two near-by points on the same cluster at the percolation threshold. Our data are based on a new and very efficient algorithm. For $d=2$ they clearly…
We study moderate deviations from hydrodynamic limits of a reaction diffusion model. The process is defined as the superposition of the symmetric exclusion process with a Glauber dynamics. When the process starts from a product measure with…
The Bures-Hall distance metric between quantum states is a unique measure that satisfies various useful properties for quantum information processing. In this work, we study the statistical behavior of quantum entanglement over the…
Motivated by the problem of computing the distribution of the largest distance $d_{\max}$ between $n$ random points on a circle we derive an explicit formula for the moments of the maximal component of a random vector following a Dirichlet…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein…
In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in…