相关论文: Combinatorial aspects of matrix models

We compute the model-independent contributions to the primordial bispectrum and trispectrum in de Sitter space due to high-energy physics. We do this by coupling a light inflaton to an auxiliary heavy field, and then evaluating correlation…

We study symplectic properties of the monodromy map of the Schr\"odinger equation on a Riemann surface with a meromorphic potential having second-order poles. At first, we discuss the conditions for the base projective connection, which…

We consider Schr\"odinger equations and Fokker-Planck equations in one dimension, and study the low-energy asymptotic behavior of the Green function using a new method. In this method, the coefficient of the expansion in powers of the wave…

Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…

The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The…

Free energy functionals of Ginzburg-Landau type lie at the heart of a broad class of continuum dynamical models, such as the Cahn-Hilliard and Swift-Hohenberg equations. Despite the wide use of such models, the assumptions embodied in the…

Working in a sector of large charge is a powerful tool to analytically access models that are either strongly coupled or otherwise difficult to solve explicitly. In the context of integrable systems, Volin's method is exactly such a…

A method for solving Schwinger-Dyson equations for the Green function generating functional of non-Abelian gauge theory is proposed. The method is based on an approximation of Schwinger-Dyson equations by exactly soluble equations. For the…

In this paper, we introduce the notion of a grammatical labeling to describe a recursive process of generating combinatorial objects based on a context-free grammar. For example, by labeling the ascents and descents of a Stirling…

The problem of a calculation of parameters of the Standard Model is considered in the framework of the compensation approach. Conditions for a spontaneous generation of effective interactions of fundamental fields are shown to lead to sets…

Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence with planar Eulerian (i.e., bicolored) maps.…

Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding…

In this paper we derive a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large $N$, of the logarithm of the partition function of $N \times N$ Hermitian random matrices. These…

We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new…

In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…

The operator expansion of free Green function of Helmholtz equation for arbitrary N- dimension space leads to asymptotic extension of 3- dimension Grimus-Stockinger formula closely related to multipole expansion. Analytical examples…

We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…