Related papers: Random sets of finite perimeter
We are concerned with unbounded sets of $\mathbb{R}^N$ whose boundary has constant nonlocal (or fractional) mean curvature, which we call CNMC sets. This is the equation associated to critical points of the fractional perimeter functional…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
We describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process. We characterize those stationary processes with finite second moment for which, after…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all…
We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the…
We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the…
Random point fields which describe gases consisting of para-particles of any order are given by means of the canonical ensemble approach. The analysis for the cases of the para-fermion gases are discussed in full detail.
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
We prove the Central Limit Theorem and superpolynomial mixing for environment viewed for the particle process in quasi periodic Diophantine random environment. The main ingredients are smoothness estimates for the solution of the Poisson…
This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in R^p as the number of points n -> infinity, while the dimension p is either fixed or growing with n. For both…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that…
We establish some relations between the perimeter, the area and the visual angle of a planar compact convex set. Our first result states that Crofton's formula is the unique universal formula relating the visual angle, length and area.…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…
The study of substructures in random objects has a long history, beginning with Erd\H{o}s and R\'enyi's work on subgraphs of random graphs. We study the existence of certain substructures in random subsets of vector spaces over finite…
This paper introduces almost partitionable sets to generalize the known concept of partitionable sets. These notions provide a unified frame to construct $\mathbb{Z}$-cyclic patterned starter whist tournaments and cyclic balanced sampling…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…