Related papers: A remark on Jacobi ensemble
We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses…
We consider expansive homeomorphisms with the specification property. We give a new simple proof of a large deviation principle for Gibbs measures corresponding to a regular potential and we establish a general symmetry of the rate function…
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due to…
We prove large deviation principles for the distribution of the empirical measure of the eigenvalues of Lax matrices following the Generalized Gibbs ensembles of the classical Toda chain introduced in [10]. We deduce the almost sure…
We prove a uniformization theorem in complex algebraic geometry.
For axiom A diffeomorphisms and equilibrium state, we prove a Large deviation result for the sequence of successive return times into a fixed open set, under some assumption on the boundary. Our result relies on and extends the work by…
In this paper, we establish a large deviation principle for stochastic evolution equations with reflection in an infinite dimensional ball. Weak convergence approach plays an important role.
We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$…
Jacobi permutations, introduced by Viennot in the context of Jacobi elliptic functions, are counted by the Euler numbers $E_{n}$ appearing in the series expansion $\sec x+\tan x=\sum_{n=0}^{\infty}E_{n}x^{n}/n!$. We conduct a systematic…
In view of the recent interest in a short proof of the Jacobi identity for the Poisson-brackets, we provide an alternative simple proof for the same. Our derivation is based on the validity of the Leibnitz rule in the context of dynamical…
The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of…
We devise an abstract, modular scheme to prove continuity of the Lyapunov exponents for a general class of linear cocycles. The main assumption is the availability of appropriate large deviation type (LDT) estimates which are uniform in the…
We provide the large deviation principle for higher dimensional piecewise expanding maps and by using the functional approach of Hennion and Herv\'e, slightly modified.
We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…
In this paper universality limits are studied in connection with measures which exhibit power-type singular behavior somewhere in their support. We extend the results of Lubinsky for Jacobi measures supported on $ [-1,1] $ to generalized…
We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in…
We give a simple and entirely elementary proof of Gasper's theorem on the Markov sequence problem for Jacobi polynomials. It is based on the spectral analysis of an operator that arises in the study of a probabilistic model of colliding…
In this paper, we give an expository presentation of the paper of Olivier Mathieu. The paper of Mathieu proves that a Lie group-theoretic conjecture implies the Jacobian Conjecture. To give Mathieu's proof, we first review the required…