Related papers: The complex behaviour of Galton rank order statist…
For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics $P(s)\propto \exp(-A s^{2-\gamma })$ for $s\gg \av{s}\equiv 1$ which is universal and intermediate between the…
Ordinal categorical data are widely collected in psychology, education, and other social sciences, appearing commonly in questionnaires, assessments, and surveys. Latent class models provide a flexible framework for uncovering unobserved…
We study rates asymptotic of transformations between entangled states by local operations and classical communication and a sublinear amount of quantum communication. It is known that additive asymptotically continuous entanglement measures…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…
Selection systems and the corresponding replicator equations model the evolution of replicators with a high level of abstraction. In this paper we apply novel methods of analysis of selection systems to the replicator equations. To be…
In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish…
The rank-based association between two variables can be modeled by introducing a latent normal level to ordinal data. We demonstrate how this approach yields Bayesian inference for Kendall's rank correlation coefficient, improving on a…
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…
The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric,…
In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models of https://arxiv.org/abs/1601.05770. We define operators, inspired by the…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…
We study the harmonic moments of Galton-Watson processes, possibly non homogeneous, with positive values. Good estimates of these are needed to compute unbiased estimators for non canonical branching Markov processes, which occur, for…
A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
Let A be a minor-closed class of labelled graphs, and let G_n be a random graph sampled uniformly from the set of n-vertex graphs of A. When n is large, what is the probability that G_n is connected? How many components does it have? How…
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…