10 citations · 17 across the 10 of their papers we have counts for
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Continuity of Zero-Hitting Times of Bessel Processes and Welding Homeomorphisms of SLE
Dmitry Beliaev, Atul Shekhar, Vlad Margarint
We consider a family of Bessel Processes that depend on the starting point and dimension , but are driven by the same Brownian motion. Our main result is that almost surely…
Continuity in in theory using a constructive method and Rough Path Theory
Dmitry Beliaev, Terry J. Lyons, Vlad Margarint
Questions regarding the continuity in of the traces and maps appear very naturally in the study of SLE. In order to study the first question, we consider a natural coup…
A new approach to SLE phase transition
Dmitry Beliaev, Terry J. Lyons, Vlad Margarint
It is well know that curves exhibit a phase transition at . For they are simple curves with probability one, for they are not. The standard proof is bas…
Coupling of stationary fields with application to arithmetic waves
Dmitry Beliaev, Riccardo W. Maffucci
In this paper we obtain a range of quantitative results of the following type: given two centered Gaussian fields with close covariance kernels we construct a coupling such that th…
No repulsion between critical points for planar Gaussian random fields
Dmitry Beliaev, Valentina Cammarota, Igor Wigman
We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correl…
Intermediate and small scale limiting theorems for random fields
Dmitry Beliaev, Riccardo W. Maffucci
In this paper we study the nodal lines of random eigenfunctions of the Laplacian on the torus, the so called 'arithmetic waves'. To be more precise, we study the number of intersec…