Related papers: Large Deviation For Outlying Coordinates in Beta E…
We consider the multi-parameter random simplicial complex as a higher dimensional extension of the classical Erd\"os-R\'enyi graph. We investigate appearance of "unusual" topological structures in the complex from the point of view of large…
Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to…
We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets $K$ of ${\bf C}$ with weakly admissible external fields $Q$ and very general…
We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…
We study the beta-ensemble that represents conformal blocks of Liouville theory on the sphere. This quantity is related through AGT conjecture to the Nekrasov instanton partition function of 4d $\mathcal{N}=2$ SU(2) gauge theory with four…
We study Mallows random permutations conditioned to avoid a given pattern $\alpha$ of length~$3$. When the bias parameter is of the form $e^{\beta/n}$, we prove that these permutations converge to a non-trivial explicit deterministic…
In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of…
The frequentist interpretation of measurement results requires the specification of an ensemble of independent replications of the same experiment. For complex calculations of bias, coverage, significance, etc., this ensemble is often…
We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [17] for spectral measures of classical ensembles (Gauss-Hermite, Laguerre,…
We consider $\beta$-Jacobi ensembles with parameters $p_1, p_2\geq n.$ We prove that the empirical measure of the rescaled Jacobi ensembles converges weakly to a modified Watcher law via the spectral measure method, which revisits the weak…
We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems,…
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…
The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
Let $\Sigma_{A}(\mathbb{N})$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\mathbb{N}$ and $f: \Sigma_{A}(\mathbb{N}) \rightarrow \mathbb{R}$ a potential satisfying the Walters condition with…
This paper proves a matrix model for the Wishart Ensemble with general covariance and general dimension parameter beta. In so doing, we introduce a new and elegant definition of Jack polynomials.
This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a…
We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the…