Related papers: Stochastic integrability and the KPZ equation
We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal…
Stochastic integrals are defined with respect to a collection $P = (P_i; \, i \in I)$ of continuous semimartingales, imposing no assumptions on the index set $I$ and the subspace of $\mathbb{R}^I$ where $P$ takes values. The integrals are…
This article is based on recent works done in collaboration with M. Mintchev, E. Ragoucy and P. Sorba. It aims at presenting the latest developments in the subject of factorization for integrable field theories with a reflecting and…
This paper gives an introduction to some of the statistical physics problems which appear in the study of structural glasses. It is a shortened and updated version of a more detailed review paper which has appeared in cond-mat/0005173.
We prove quenched stochastic homogenization for divergence-form elliptic equations, under the assumption that the coefficients are stationary, ergodic, integrable, and satisfy a coarse-grained ellipticity assumption. The ellipticity…
We give a somewhat informal introduction to the integrable systems approach to the Schottky problem, explaining how the theta functions of Jacobians can be used to provide solutions of the KP equation, and culminating with the exposition of…
A stochastic approach is implemented to address the problem of a marine structure exposed to water wave impacts. The focus is on (i) the average frequency of wave impacts, and (ii) the related probability distribution of impact kinematic…
Connections of KP, qKP, and Moyal type dKP constructions are developed. Some expansion of the Moyal KP procedures of Kemmoku-Saito is given with clarification of the role of spectral variables as a phase space.
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
We introduce an integrable stochastic process associated with the $D_2$ quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the model under three types of boundary…
A representation of heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. It is demonstrated that any instance of…
We observe that Dickey's stabilizing chain can be naturally included into two-dimensional chain of infinitely many copies of equations of KP hierarchy.
We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.
Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.
Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and Kardar-Parisi-Zhang (KPZ) universality class has emerged. Theoretical developments…
The Jacobian algebras are introduced and their various properties are studied.
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…