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In this note, we study the asymptotics of an integral on the unitary group first proposed by Mergny and Potters as a multiplicative counterpart to the well-known Harish-Chandra Itzykson Zuber integral. In particular we prove in a mathematically rigorous manner a result from Mergnys and Potterss original paper in the case $beta =1,2$ and we generalize it for multiple arguments.
We investigate generalizations of the Cramer theorem. This theorem asserts that a Gaussian random variable can be decomposed into the sum of independent random variables if and only if they are Gaussian. We prove asymptotic counterparts of such decom
The stochastic Landau-Lifshitz-Bloch equation describes the phase spins in a ferromagnetic material and has significant role in simulating heat-assisted magnetic recording. In this paper, we consider the deviation of the solution to the 1-D stochasti
We develop a method for evaluating asymptotics of certain contour integrals that appear in Conformal Field Theory under the name of Dotsenko-Fateev integrals and which are natural generalizations of the classical hypergeometric functions. We illustra
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference Hamiltonian equations. We establish relations of these notions to $q$-d
In this article, we develop a framework to study the large deviation principle for matrix models and their quantiz