Related papers: A remark on Jacobi ensemble

We study Jacobi matrices on trees with one end at inifinity. We show that the defect indices cannot be greater than 1 and give criteria for essential selfadjointness. We construct certain polynomials associated with matrices, which mimic…

The proof of the Jacobi property of the guiding-center Vlasov-Maxwell bracket underlying the Hamiltonian structure of the guiding-center Vlasov-Maxwell equations is presented.

This work concerns about stochastic Burgers type equations with reflection. First of all, by means of the equicontinuous uniform Laplace principle, we prove the Freidlin-Wentzell uniform large deviation principle for these equations…

The Jacobi polynomial has been advocated by many authors as a useful tool to evolve non-singlet structure functions to higher $Q^2$. In this work, it is found that the convergence of the polynomial sum is not absolute, as there is always a…

The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…

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 present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the…

We prove a large deviation principle for the sequence of push-forwards of empirical measures in the setting of Riesz potential interactions on compact subsets K in R^d with continuous external fields. Our results are valid for base measures…

This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.

A vector variational principle is proved.

In this paper we establish the large deviation principle for the stochastic quasi-geostrophic equation in the subcritical case with small multiplicative noise. The proof is mainly based on the stochastic control and weak convergence…

We prove an inequality for Jacobi polynomials that \begin{align} \Delta_n(x):=P_n^{(\alpha_n,\beta_n)}(x)P_n^{(\alpha_{n+1},\beta_{n+1})}(x)- P_{n-1}^{(\alpha_n,\beta_n)}(x)P_{n+1}^{(\alpha_{n+1},\beta_{n+1})}(x)\le 0,\ \forall x\ge 1,…

We define certain extensions of Jacobi groups of $A_n$, prove an analogue of Chevalley Theorem for their invariants, and construct a Dubrovin Frobenius structure on it orbit space.

We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several…

We consider Jack measures on partitions with homogeneous defining specializations. For each of the six distinct classes of measures obtained this way we prove a global law of large numbers with an explicit limiting particle density. We also…

We prove a large deviation principle for the point process of large Poisson $k$-nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point process of unit intensity in a growing sampling window in…

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we…

We prove an energy estimate for the polar empirical measure of the two-dimensional symmetric simple exclusion process. We deduce from this estimate and from results in reference [2] large deviations principles for the polar empirical…

In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability…