arXiv subjects

Alexey Tochin

Publications and source records attributed to Alexey Tochin.

3 recordsLinked to original sources

arXiv2016

Coupling of Gaussian free field with general slit SLE

We consider a coupling of the Gaussian free field with slit holomorphic stochastic flows, called ($δ,σ$)-SLE, which contains known SLE processes (chordal, radial, and dipolar) as particular cases. In physical terms, we study a free boundary conformal field theory with one scalar bosonic field, where Green's function is assumed to have some general regular harmonic part. We establish which of these models allow coupling with ($δ,σ$)-SLE, or equivalently, when the correlation functions induce local ($δ,σ$)-SLE martingales (martingale observables).

math.PR↗

arXiv2016

General Slit Stochastic Löwner Evolution and Conformal Field Theory

This monograph is dedicated to a generalization of the Löwner equation in its stochastic form known as SLE and to its coupling with the Gaussian free field, ultimately aiming at the construction of a boundary conformal field theory with one free scalar bosonic field. This study is presented in line with a systematic, and hopefully concise, presentation and generalization of known elements of the theory of Löwner evolution. We also study the relation to singular representations of the Virasoro algebra and methods of numerical simulation. The main results are in the proof of the basic properties of the generalized SLE and general necessary and sufficient conditions for the coupling. We also introduce a machinery that possesses to consider all Löwner equations and known types of the coupling as different manifestations of the same thing.

math-ph↗

arXiv2014

General slit Löwner chains

We use general Löwner theory to define general slit Löwner chains in the unit disk, which in the stochastic case lead to slit holomorphic stochastic flows. Radial, chordal and dipolar SLE are classical examples of such flows. Our approach, however, allows to construct new processes of SLE type that possess conformal invariance and the domain Markov property.The local behavior of these processes is similar to that of the classical SLE.

math.CV↗