Related papers: Combinatorial aspects of matrix models
Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain…
The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order.…
The generating functional for scalar theories admits a representation which is dual with respect to the one introduced by Schwinger, interchanging the role of the free and interacting terms. It maps $\int V(\delta_J)$ and $J\Delta J$ to…
We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary…
We consider two different genus expansions of the free energy functions of Hermitian one-matrix models, one using fat graphs, one using ordinary graphs (thin graphs). Some structural results are first proved for the thin version of genus…
We study the map from conductances to edge energies for harmonic functions on finite graphs with Dirichlet boundary conditions. We prove that for any compatible acyclic orientation and choice of energies there is a unique choice of…
The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating…
We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity. In particular, this result explains the counterintuitive phenomenon that…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet…
We express the nonlocal BMS charges of a free massless Klein-Gordon scalar field in 2+1 in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic…
Motivated by questions arising in the study of harmonic maps and Yang Mills theory, we study new techniques for producing optimal monotonicity relations for geometric partial differential equations. We apply these results to sharpen epsilon…
The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…
Coloured graphical models are Gaussian statistical models determined by an undirected coloured graph. These models can be described by linear spaces of symmetric matrices. We outline a relationship between the symmetries of the graph and…
The connection between matrix integrals and links is used to define matrix models which count alternating tangles in which each closed loop is weighted with a factor n, i.e. may be regarded as decorated with n possible colors. For n=2, the…
Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be…
A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…