相关论文: Pins, Stakes, Anchors and Gaussian Triangles
Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.
The inertial and gravitational properties of intrinsic spin are discussed and some of the recent work in this area is briefly reviewed. The extension of relativistic wave equations to accelerated systems and gravitational fields is…
Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects, and on the grain/fluid density ratio r. In gas (r >> 1…
We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
These lectures give an introduction to Gravitational Lensing. We discuss lensing by point masses, lensing by galaxies, and lensing by clusters and larger-scale structures in the Universe. The relevant theory is developed and applications to…
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields…
Recent work has addressed the problem of inferring Langevin dynamics from data. In this work, we address the problem of relating terms in the Langevin equation to statistical properties, such as moments of the probability density function…
We study the probabilistic properties of the Greatest Increase Grid (GIG) digraph. We compute the probability of a particular sequence of directed edges connecting two random vertices. We compute the joint probability that a set of vertices…
Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic…
We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
Gaussian random vectors exhibit the loss of dimension phenomena, which relate to their joint survival tail behaviour. Besides, the fact that the components of such vectors are light-tailed complicates the approximations of various…
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
The first part of these lectures contains an introductory review of the AdS/CFT duality and of its tests. Applications to thermal gauge theory are also discussed briefly. The second part is devoted to a review of gauge-string dualities…
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new…
The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The…
We address the problem of measuring the relative angle between two "quantum axes" made out of N1 and N2 spins. Closed forms of our fidelity-like figure of merit are obtained for an arbitrary number of parallel spins. The asymptotic regimes…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
Statistical properties of random cross-correlated sequences constructed by the convolution method (likewise referred to as the Rice's or the inverse Fourier transformation) are examined. Algorithms for their generation are discussed. They…