16 citations · 34 across the 13 of their papers we have counts for
16 papers
Locally finite fixed points of branching Brownian motion
Xinxin Chen, Arnab Chowdhury, Atul Shekhar +1
We give a full characterization of the fixed points of Branching Brownian motion with critical and supercritical drifts under no additional assumptions besides it being locally fin…
Asymptotics of the Number of Components of Random Polynomial Lemniscates
Subhajit Ghosh, Koushik Ramachandran, Atul Shekhar
Consider a sequence of random polynomials , where are i.i.d. random variables distributed uniformly on the unit disc . Le…
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…
Domain of attraction of the fixed points of Branching Brownian motion
Xinxin Chen, Christophe Garban, Atul Shekhar
We give a complete characterisation of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a…
On Loewner chains driven by semimartingales and complex Bessel-type SDEs
Vlad Margarint, Atul Shekhar, Yizheng Yuan
We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show…
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…
Remarks on the regularity of quasislits
Lukas Schoug, Atul Shekhar, Fredrik Viklund
A quasislit is the image of a vertical line segment [0, iy], y > 0, under a quasiconformal homeomorphism of the upper half-plane fixing infinity. Quasislits correspond precisely to…
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…
Remarks on Loewner Chains Driven by Finite Variation Functions
Atul Shekhar, Huy Tran, Yilin Wang
To explore the relation between properties of Loewner chains and properties of their driving functions, we study Loewner chains driven by functions of finite total variation. U…
Smoothness of Flow and Path-by-Path Uniqueness in Stochastic Differential Equations
Siva Athreya, Suprio Bhar, Atul Shekhar
We consider the stochastic differential equation with , , $f: \mathbb{R}^d \rightarrow…
On the existence of SLE trace: finite energy drivers and non-constant
Peter K. Friz, Atul Shekhar
Existence of Loewner trace is revisited. We identify finite energy paths (the "skeleton of Wiener measure") as natural class of regular drivers for which we find simple and natural…
General Rough integration, Levy Rough paths and a Levy--Kintchine type formula
Peter Friz, Atul Shekhar
We consider rough paths with jumps. In particular, the analogue of Lyons' extension theorem and rough integration are established in a jump setting, offering a pathwise view on sto…
Doob--Meyer for rough paths
Peter Friz, Atul Shekhar
Recently, Hairer--Pillai proposed the notion of -roughness of a path which leads to a deterministic Norris lemma. In the Gubinelli framework (Hoelder, level 2) of rough paths, t…