Related papers: Branching Formula for $q$-Toda Function of Type B

In this article we extend B. Simon's construction and results for leading order eigenvalue asymptotics to $n$-dimensional Schr\"odinger operators with non-confining potentials given by: $H^\alpha_n=-\Delta +\prod\limits_{i=1}^n…

We present an elementary derivation of the soliton-like solutions in the $A_n^{(1)}$ Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are…

We construct an integral representation of eigenfunctions for Macdonald's $q$-difference operator associated with the root system of type $C_n .$ It is given in terms of a restriction of a $q$-Jordan-Pochhammer integral. Choosing a suitable…

We consider functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\be,1}^1(\R^2)$, then we have the following…

This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an investigation initiated and developed in a…

We consider the epsilon-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these…

Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous…

A reduction formula for the branching coefficients of tensor products of representations and more generally restrictions of representations of a semisimple group to a semisimple subgroup is proved in work by Knutson-Tao and Derksen-Weyman.…

The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic functions have asymptotically independent summands. It is…

The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-analogue of the Schur function $s_\lambda(\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial…

In this paper we introduce a class of generalized supersymmetric Toda field theories. The theories are labeled by a continuous parameter and have $N=2$ supersymmetry. They include previously known $N=2$ Toda theories as special cases. Using…

In this paper we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or…

We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For this family we prove a skew Schur function expansion…

We obtain a representation formula for the derivative of the spectral shift function $\xi(\lambda; B, \epsilon)$ related to the operators $H_0(B,\epsilon) = (D_x - By)^2 + D_y^2 + \epsilon x$ and $H(B, \epsilon) = H_0(B, \epsilon) + V(x,y),…

Combinatorial expressions are presented to the solutions to initial value problems of the discrete and ultradiscrete Toda molecules. For the discrete Toda molecule, a subtraction-free expression of the solution is derived in terms of…

We calculate the $\beta$-functions for $SO(N)$ and $SU(N)$ gauge theories coupled to adjoint and fundamental scalar representations, correcting long-standing, previous results. We explore the constraints on $N$ resulting from requiring…

Let $m_{\lambda }$ be the monomial symmetric functions, $ \lambda $ being an integer partition of $n\in \mathbb{N}^{\ast }$. For the specialization corresponding to the $q$-deformation of the exponential, we prove that each $m_{\lambda }$…

In this paper, we give a simple proof of the functional relation for the Lerch type Tornheim double zeta function. By using it, we obtain simple proofs of some explicit evaluation formulas for double $L$-values.

Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics…

Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the $\tau$ functions for the Painlev\'e equations is also discussed.