Titlebook: Asymptotic Combinatorics with Application to Mathematical Physics; Vadim Malyshev,Anatoly Vershik Book 2002 Kluwer Academic Publishers 200

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Limpid

Introduction to Matrix Models Schr?dinger equation, in which the forces between the nucleons are not very well-known, and whose solution requires drastic simplifying assumptions, a simple random Hamiltonian drawn from a Gaussian ensemble. The only constraints are imposed by symmetries, such as time-reversal symmetry, and the ne

anthesis

A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structuresly in elementary functions. The support of the density consists generically from . intervals. We introduce also certain .-periodic real symmetric Jacobi matrices and we give formulas relating the limiting eigenvalue density and the potential of the considered random matrix ensembles with the density

Rodent

The Combinatorics of Alternating Tangles: From Theory to Computerized Enumerationmponent, and in particular the limit . → 0 yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two types of vertices (self-intersections and tangencies), w

IVORY

Invariance Principles for Non-Uniform Random Mappings and Treesng that many . → ∞ limit distributions can be described as distributions of suitable functions of reflecting Brownian bridge. To study non-uniform cases, in this paper we formulate a . in terms of iterates of a fixed number of random elements. We show that the sampling invariance principle implies m

Vulnerary

沖突

Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2Dport, we establish implicit equations for these functions. After solving the combinatorial problems, we introduce an approximation allowing to reduce these equations to a set of linear equations for a finite number of unknown functions. Imposing natural conditions, we obtain a closed system of linea

寒冷

Notes on Homogeneous Vector Bundles over Complex Flag Manifoldsundle over the flag manifold . = ./. corresponding to a linear representation. of .. Using Bott’s theorem, we obtain sufficient conditions on . in terms of the combinatorial structure of . for cohomology groups ..(.,..) to be zero, where .. is the sheaf of holomorphic sections of ... In particular,

Nibble

Representations Theory and Doubles of Yangians of Classical Lie Superalgebrasof quantization of the Lie superbialgebra of polynomial loops. Two systems of generators and defining relations are introduced, and their equivalence is proved. The PBW theorem for the Yangians of classical Lie superalgebras is formulated and proved. All irreducible finite-dimensional representation

Alveoli

Idempotent (Asymptotic) Mathematics and the Representation TheoryMathematics as the Planck constant tends to zero taking pure imaginary values. In the framework of Idempotent Mathematics some basic concepts and results of the theory of group representations (including some unexpected theorems of the Engel type) are discussed.