相关论文: Toeplitz determinants, random growth and determina…

We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.

This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…

We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…

This is a survey of old and new problems and results in additive number theory.

Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…

In this paper we investigate Toeplitz and symmetric Toeplitz determinants of inverse functions for some classes of univalent functions and improve some previous results.

This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for…

We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…

In the first part of this survey, we present classical notions arising in combinatorics on words: growth function of a language, complexity function of an infinite word, pattern avoidance, periodicity and uniform recurrence. Our…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of cumulants in probability theory. We review this theory, and…

Combinatorial groups together with the groups of natural coalgebra transformations of tensor algebras are linked to the groups of homotopy classes of maps from the James construction to a loop space. This connection gives rise to…

We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local…

We will study the relationship between two well-known theories, genetic evolution and random matrix theory in the context of many-body systems. It is suggested that genetic evolution can be described by a random matrix theory with…

Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinear partial differential equations.…

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…

This is survey of some recent results connecting random matrices, non-colliding processes and queues.

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…