Related papers: Multi-matrix models without continuum limit
A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden…
We describe how to implement the time-dependent variational principle for matrix product states in the thermodynamic limit for nonuniform lattice systems. This is achieved by confining the nonuniformity to a (dynamically growable) finite…
An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We also consider one-variable reductions of the dispersionless DKP hierarchy and…
An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
Traditionally, the geometric multigrid method is used with nested levels. However, the construction of a suitable hierarchy for very fine and unstructured grids is, in general, highly non-trivial. In this scenario, the non-nested multigrid…
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line…
Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as "the coupled KP hierarchy" and "the Pfaff lattice"). Those results are now extended to a Toda version of the DKP hierarchy (tentatively…
Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…
We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of W-operators. A number of illustrations is given, including the Gaussian Hermitian matrix model, Hermitian model in…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
We review the recent approach to the construction of (3+1)-dimensional integrable dispersionless partial differential systems based on their contact Lax pairs and the related $R$-matrix theory for the Lie algebra of functions with respect…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…