4 citations · 7 across the 4 of their papers we have counts for
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Large Deviation Principle for complex solution to squared Bessel SDE
Arnab Chowdhury, Atul Shekhar
Complex solutions to squared Bessel SDEs appear naturally in relation to Schramm-Loewner evolutions. We prove a large deviation principle for such solutions as the dimension parame…
The fixed points of Branching Brownian Motion
Xinxin Chen, Christophe Garban, Atul Shekhar
In this work, we characterize all the point processes on which are left invariant under branching Brownian motions with critical dri…
A new proof of Liggett's theorem for non-interacting Brownian motions
Xinxin Chen, Christophe Garban, Atul Shekhar
In this note, we give a new proof of Liggett's theorem on the invariant measures of independent particle systems from [Lig78] in the particular case of independent drifted Brownian…
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…
Complex Solutions to Bessel SDEs and SLEs
Atul Shekhar, Vlad Margarint
We consider a variant of Bessel SDE by allowing the solution to be complex valued. Such SDEs appear naturally while studying the trace of Schramm-Loewner-Evolutions (SLE). We estab…
Smoothing of Boundary Behaviour in Stochastic Planar Evolutions
Atul Shekhar
Motivated by the study of trace for Schramm-Loewner evolutions, we consider evolutions of planar domains governed by ordinary differential equations with holomorphic vector fields…