Related papers: Stochastic integrability and the KPZ equation
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms becoming ill-defined. Besides the theories of regularity…
In this paper we present a survey on recent developments in the study of ambit fields and point out some open problems. Ambit fields is a class of spatio-temporal stochastic processes, which by its general structure constitutes a flexible…
A recently developed treatment of stochastic processes leads to the construction of a potential landscape for the dynamical evolution of complex systems. Since the existence of a potential function in generic settings has been frequently…
A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class -- those featuring a wide gap between the long timescales over which constraints…
This note gathers what is known about, and provides some new results concerning the operations of intersection, of ``generated $\sigma$-field'', and of ``complementation'' for (independent) complete $\sigma$-fields on probability spaces.
Some new integrals involving the Stieltjes constants are developed in this paper.
The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system is described. For the standard two-fold elliptic coverings the…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Complex Schroedinger equation is transformed to spinor or coupled scalar field equations replacing the imaginary unit $i$ by a matrix $\begin{bmatrix} 0 & 1 \\-1 & 0 \end{bmatrix}$. New perspecive on stochasic approach is developed with…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past…
Cosmological solutions of Einstein's equations for equilibrium statistical systems of particles with scalar interaction are investigated. It is shown that the scalar field can effectively change the state equation of a statistical system,…
The property of isoscaling in nuclear fragmentation is studied using a simple bond percolation model with ``isospin'' added as an extra degree of freedom. It is shown analytically, first, that isoscaling is expected to exist in such a…
Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge…
We construct explicit equations of Cartwright-Steger and related surfaces.
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…