相关论文: Cover levels and random interlacements

We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z^d, d bigger or equal to 3. A non-negative parameter u measures how many trajectories enter the picture. This model describes in the…

We study Lam's reduced random walk in a hyperbolic triangle group, which we view as a random walk in the upper half-plane. We prove that this walk converges almost surely to a point on the extended real line. We devote special attention to…

Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting…

In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show,…

A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…

We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These…

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…

We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use…

We investigate the distribution of the eigenvalues of the reduced density matrix (entanglement spectrum) after a global quantum quench. We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits…

In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the interacting resonant level model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results…

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…

We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…

A previously introduced real space renormalization-group treatment of the random transverse-field Ising spin chain is extended to provide detailed information on the distribution of the energy gap and the end-to-end correlation function for…

A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…

We investigate the problem of generating common randomness (CR) from finite compound sources aided by unidirectional communication over rate-limited perfect channels. The two communicating parties, often referred to as terminals, observe…

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…

In this paper we investigate the level sets of extremal Sobolev functions for subcritical exponents p. We conjecture that as p increases the corresponding extremal functions become more peaked, which we can measure by comparing their…