Related papers: Stochastic integrability and the KPZ equation
We provide a new characterization of the logarithmic Sobolev inequality.
We propose a consistently algebraic formulation of the extended KP (supersymmetric) integrable -hierarchy systems. We exploit the results already established in [14] and which consist in a framework suspected to unify in a fascinating way…
We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
This survey provides an introduction to the Stolz-Teichner program on elliptic cohomology and quantum field theory.
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with the $(1+1)$ dimensional Kardar-Parisi-Zhang equation. In the present paper, the analytical results obtained there in…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
This is a survey on stated skein algebras and their representations.
The paper considers a stochastic differential equation of Duffing type with Markov coefficients. The existence of unpredictable solutions is considered. The unpredictability is a property of bounded functions characterized by unbounded…
Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…
A detailed analysis of conditions on 2-body interaction potential, which ensure stability, superstability or strong superstability of statistical systems is given. There has been given the connection between conditions of superstability…
In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves…
We prove a convergence result for a large class of random models that encompasses the case of the BPHZ models used in the study of singular stochastic PDEs. We introduce for that purpose a useful variation on the notion of regularity…
Opposing to a (common) belief against the existence of a thermodynamic-like potential for the KPZ equation, here we present a derivation for such a functional. With its knowledge we prove some global shift invariance properties previously…
The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power some of these methods have become prominent and central to modern data analysis.…
The past two decades have seen a revolution in statistical physics, generalizing it to apply to systems of arbitrary size, evolving while arbitrarily far from equilibrium. Many of these new results are based on analyzing the dynamics of the…
We consider a Hamiltonian system which has its origin in a generalization of exact renormalization group flow of matrix scalar field theory and describes a non-linear generalization of the shock-wave equation that is known to be integrable.…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…