相关论文: On the Large N Limit of the Itzykson-Zuber Integra…
A new scaling regime characterized by a $z=1$ dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations. In these works, this scaling, differing…
Using the collective field theory approach of large-N generalized two-dimensional Yang-Mills theory on cylinder, it is shown that the classical equation of motion of collective field is a generalized Hopf equation. Then, using the…
We systematically analyze the large-$N$ limit of the superconformal index of $\mathcal{N}=1$ superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate…
The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…
A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated.…
We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one can reduce the matrix integral to the…
We reconsider the large $N$ asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary…
We examine the properties of observables in the Kazakov-Migdal model. We present explicit formulae for the leading asymptotics of adjoint Wilson loops as well as some other observables for the model with a Gaussian potential. We discuss the…
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally…
An integro-differential equation satisfied by an eigenvalue density defined as the logarithmic derivative of the average inverse characteristic polynomial of a Wilson loop in two dimensional pure Yang Mills theory with gauge group SU(N) is…
The inviscid Burgers equation with random and spatially smooth forcing is considered in the limit when the size of the system tends to infinity. For the one-dimensional problem, it is shown both theoretically and numerically that many of…
Character expansions are among the most important approaches to modern quantum field theory, which substitute integrals by combinations of peculiar special functions from the Schur-Macdonald family. These formulas allow various…
It is shown that the correlation functions of the random variables $\det(\lambda - X)$, in which $X$ is a real symmetric $ N\times N$ random matrix, exhibit universal local statistics in the large $N$ limit. The derivation relies on an…
In this work, we consider the stochastic Burgers-Huxley equation perturbed by multiplicative Gaussian noise, and discuss about the global solvability results and asymptotic behavior of solutions. We show the existence of a global strong…
We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brezin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal…
We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of…
We compute the Itzykson-Zuber (IZ) integral for the superunitary group U(m|n). As a consequence, we are able to find the non-zero correlations of superunitary matrices
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the…
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…