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math.PR2020
Brownian motion can feel the shape of a drum
Renan Gross
We study the scenery reconstruction problem on the -dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycl…
math.PR2019
Concentration on the Boolean hypercube via pathwise stochastic analysis
Ronen Eldan, Renan Gross
We develop a new technique for proving concentration inequalities which relate between the variance and influences of Boolean functions. Using this technique, we 1. Settle a conjec…
math.PR2019
A conformal Skorokhod embedding
Renan Gross
Start a planar Brownian motion and let it run until it hits some given barrier. We show that the barrier may be crafted so that the x coordinate at the hitting time has any prescri…