5 papers
Noise sensitivity from fractional query algorithms and the axis-aligned Laplacian
Renan Gross
We introduce the notion of classical fractional query algorithms, which generalize decision trees in the average-case setting, and can potentially perform better than them. We show…
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…
A phase diagram for bacterial swarming
Avraham Be`er, Bella Ilkanaiv, Renan Gross +4
Bacterial swarming is a rapid mass-migration, in which thousands of cells spread collectively to colonize a surface. Physically, swarming is a natural example of active particles t…
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…
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…