Related papers: Universal correlators for multi-arc complex matrix…

Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We…

An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.

We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential…

We derive the loop equation for the 1-matrix model with generic difference-type measure for eigenvalues and develop a recursive algebraic framework for solving it to an arbitrary order in the coupling constant in and beyond the planar…

By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…

We prove that for Gaussian random normal matrices the correlation function has universal behavior. Using the technique of orthogonal polynomials and identities similar to the Christoffel-Darboux formula, we find that in the limit, as the…

All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents…

We studied the universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues. We studied the asymptotic limit when the number of both eigenvalues goes to infinity and obtained universality results. In this case, the…

We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…

We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…

We calculate genus one corrections to Hermitian one-matrix model solution with arbitrary number of cuts directly from the loop equation confirming the answer previously obtained from algebro-geometrical considerations and generalizing it to…

We present some Markovian approaches to prove universality results for some functions on the symmetric group. Some of those statistics are already studied in [Kammoun, 2018, 2020] but not the general case. We prove, in particular, that the…

I investigate universality of the two-dimensional higher-derivative conformal theory using the method of singular products. The previous results for the central charge at one loop are confirmed for the quartic and six-derivative actions.

We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant…

This paper provides the constructive loop vertex expansion for stable matrix models with (single trace) interactions of arbitrarily high even order in the Hermitian and real symmetric cases. It relies on a new and simpler method which can…

We demonstrate that the melting curves of various model systems of interacting particles collapse to (or are located very close to) a universal master curve on a plane of appropriately chosen scaled variables. The physics behind this…

We derive the analogues of the Harer-Zagier formulas for single- and double-trace correlators in the q-deformed Hermitian Gaussian matrix model. This fully describes single-trace correlators and opens a road to $q$-deformations of important…

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

We calculate wide distance connected correlators in non-gaussian orthogonal, unitary and symplectic random matrix ensembles by solving the loop equation in the 1/N-expansion. The multi-level correlator is shown to be universal in large N…