Related papers: Cubic asymmetric multitrace matrix model
We perform a high-temperature expansion of scalar quantum field theory on fuzzy CP^n to third order in the inverse temperature. Using group theoretical methods, we rewrite the result as a multitrace matrix model. The partition function of…
We study the phase diagram of the scalar field theory on the fuzzy sphere described as a particular multitrace matrix model. We consider perturbative and nonperturbative terms in the kinetic term effective action and describe consequences…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…
We study a Hermitian matrix model with a quartic potential, modified by a curvature term $\mathrm{tr}(R\Phi^2)$, where $R$ is a fixed external matrix. Inspired by the truncated Heisenberg algebra formulation of the Grosse--Wulkenhaar model,…
Ratios of quadratic forms in correlated normal variables which introduce noncentrality into the quadratic forms are considered. The denominator is assumed to be positive (with probability 1). Various serial correlation estimates such as…
We show in the example of a one-dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form. The corresponding algebra is quadratic and involves three different…
We study a Hermitian matrix model with the standard quartic potential amended by a $\mathrm{tr}(R\Phi^2)$ term for fixed external matrix $R$. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the…
We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which…
In this book we describe BMW traffic assignment model and Nesterov-dePalma model. We consider Entropy model for demand matrix. Based on this models we build multi-stage traffic assignment models. The equilibrium in such models can be found…
Quadratic matrix equations of the kind $A_1X^2+A_0X+A_{-1}=X$ are encountered in the analysis of Quasi--Birth-Death stochastic processes where the solution of interest is the minimal nonnegative solution $G$. In many queueing models,…
In this paper we consider multi-stages traffic assignment with several demand layers, user types and network types. We consider two stages: demand matrix calculation (Entropy Wilson's model) and traffic assignment models (Beckmann or…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
In this paper we examine iterative methods for solving the forward ($A{\bf x}={\bf b}$) and adjoint ($A^{T}{\bf y}={\bf g}$) systems of linear equations used to approximate the scattering amplitude, defined by ${\bf g}^{T}{\bf x}={\bf…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show that the mean number of fixed points can be calculated as the…
An attempt to merge into a single model, which reduces to the solution of non-smooth convex optimization problem: calculation model of OD-matrix (entropy model), the mode split model and the model of the equilibrium distribution of flows…
Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically…
We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to…