Related papers: Wigner- and Marchenko-Pastur-type limits for Jacob…
We study three instances of log-correlated processes on the interval: the logarithm of the Gaussian unitary ensemble (GUE) characteristic polynomial, the Gaussian log-correlated potential in presence of edge charges, and the Fractional…
The problem of conditioning on the occupation field was investigated for the Brownian motion in 1998 independently by Aldous [4] and Warren and Yor [34] and recently for the loop soup at intensity $1/2$ by Werner [35], Sabot and Tarr\`es…
We consider sample covariance matrices of the form $X^*X$, where $X$ is an $M \times N$ matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that the resolvent $(X^* X - z)^{-1}$ converges…
In this paper we consider the Witten Laplacian on 0-forms and give sufficient conditions under which the Witten Laplacian admits a compact resolvent. These conditions are imposed on the potential itself, involving the control of high order…
We consider a path-dependent Hamilton--Jacobi equation with coinvariant derivatives over the space of continuous functions. We prove two uniqueness results for viscosity (generalized) solutions defined in terms of coinvariantly smooth test…
Let $A$ and $B$ be independent, central Wishart matrices in $p$ variables with common covariance and having $m$ and $n$ degrees of freedom, respectively. The distribution of the largest eigenvalue of $(A+B)^{-1}B$ has numerous applications…
The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to \alpha$, $\alpha>0$, a scaling…
Motivated by the pseudogap-Fermi liquid transition in doped Mott insulators, we examine the excitations of a $t$-$J$ model with random and all-to-all hopping and exchange. The stability of quasiparticles such as spin-1/2 fermions, spin-1…
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…
We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter $t$ if and only if the measures come from the Meixner class. Moreover, we prove the parallel result, in a more explicit way, for…
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fej\'er monotonicity condition, in the context of a (local) compactness assumption. Our result is quantitative…
It is well-known that the semi-circle law, which is the limiting distribution in the Wigner theorem, is the minimizer of the logarithmic energy penalized by the second moment. A very similar fact holds for the Girko and Marchenko--Pastur…
This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of…
In this paper, we study the probability density function, $\mathbb{P}(c,\alpha,\beta, n)\,dc$, of the center of mass of the finite $n$ Jacobi unitary ensembles with parameters $\alpha\,>-1$ and $\beta >-1$; that is the probability that…
The study of the asymptotic distributions of zeros of generalized Jacobi polynomials with non real varying parameters, leads with quadratic differentials. In fact, the support of the limit measure of the root-counting measures sits on the…
The Bercovici-Pata bijection maps the set of classical infinitely divisible distributions to the set of free infinitely divisible distributions. The purpose of this work is to study random matrix models for free infinitely divisible…
Long-range dependence in time series may yield non-central limit theorems. We show that there are analogous time series in free probability with limits represented by multiple Wigner integrals, where Hermite processes are replaced by…
We prove a compactness and integral-representation theorem for sequences of families of lattice energies describing atomistic interactions defined on lattices with vanishing lattice spacing. The densities of these energies may depend on…
Motivated by some recent potential theoretic results on subordinate killed L\'evy processes in open subsets of the Euclidean space, we study processes in an open set $D\subset {\mathbb R}^d$ defined via Dirichlet forms with jump kernels of…
Inspired by Lehner's results on exchangeability systems we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. We show that these two…