Related papers: Stochastic integrability and the KPZ equation
A review of the superstatistics concept is provided, including various recent applications to complex systems.
The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.
In this paper, we consider a scalar stochastic balance law and gain the existence for stochastic entropy solutions. Our proof relies on the BGK approximation and the generalized It\^{o} formula. Moreover, as an application, we derive the…
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
We establish necessary and sufficient conditions for the uniform integrability of the stochastic exponential E(M).
Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone,…
The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
I give a very brief non-technical introduction to the intersection of the fields of spin systems and computational complexity. The focus is on spin glasses and their relationship to NP-complete problems.
Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
We develop notions of integrable functions within the theory of schemic motivic integration.
This article presents a construction of the concept of stochastic integration in Riemannian manifolds from a purely functional-analytic point of view. We show that there are infinitely many such integrals, and that any two of them are…
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…
This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
We consider a model of a scalar field, with dispersion relation {\omega}(k), coupled to a random medium of two level atoms. We investigate the dynamics of states with at most one quanta of excitation in the system. In a high frequency…