相关论文: Relating random matrix map enumeration to a univer…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…
We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck's generalized…
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in…
In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix - a special matrix which has only the natural numbers as entries and is closely…
In this survey we show how to produce asymptotics of determinants of structured matrices using operator theory methods. We describe the asymptotics for finite Toeplitz matrices, finite Toeplitz plus Hankel matrices and generalizations of…
The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. Our problems have a powerful relatively recent tool in common, the so-called topological recursion (TR) introduced by…
We establish universality of local eigenvalue correlations in unitary random matrix ensembles (1/Z_n) |\det M|^{2\alpha} e^{-n\tr V(M)} dM near the origin of the spectrum. If V is even, and if the recurrence coefficients of the orthogonal…
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function,also…
The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all…
It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy…
By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological spaces and asymptotic maps is enriched over the category of…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
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 write, for geometric index values, a probabilistic proof of the product formula for spherical Bessel functions. Our proof has the merit to carry over without any further effort to Bessel-type hypergeometric functions of one matrix…
The $s$-point correlation function of a Gaussian Hermitian random matrix theory, with an external source tuned to generate a multi-critical singularity, provides the intersection numbers of the moduli space for the $p$-th spin curves…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…