Related papers: The six-vertex model on random planar maps revisit…

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D…

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…

A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten…

In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…

We present a geometric approach towards derandomizing the Isolation Lemma by Mulmuley, Vazirani, and Vazirani. In particular, our approach produces a quasi-polynomial family of weights, where each weight is an integer and quasi-polynomially…

In his book on Convex Polyhedra (section 7.2), A.D. Aleksandrov raised a general question of finding variational statements and proofs of existence of polytopes with given geometric data. The first goal of this paper is to give a…

Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…

We compute the action-angle coordinates for an Ising type model whose L-operator has been previously studied in the literature by Bazhanov and Sergeev. In comparison to computations with such operators that have been examined previously by…

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given…

We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…

We give an elementary proof of a formula expressing the rotation number of a cyclic unimodular sequence of lattice vectors in terms of arithmetically defined local quantities. The formula has been originally derived by A. Higashitani and M.…

We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and…

We introduce some polynomial and analytic methods in the classification program for the complexity of planar graph homomorphisms. These methods allow us to handle infinitely many lattice conditions and isolate the new P-time tractable…

We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as…

We address a problem of covariance selection, where we seek a trade-off between a high likelihood against the number of non-zero elements in the inverse covariance matrix. We solve a maximum likelihood problem with a penalty term given by…

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

In this letter, we revisit the quantisation problem for a fundamental model of classical mechanics - the Zhukovsky-Volterra top. We have discovered a four-parametric pencil of compatible Poisson brackets, comprising two quadratic and two…

We examine and present new combinatorics for the Schur polynomials from the viewpoint of quantum integrability. We introduce and analyze an integrable six-vertex model which can be viewed as a certain degeneration model from a t-deformed…

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…