4 citations · 7 across the 9 of their papers we have counts for
12 papers
From Kreweras walks to branching perimeter processes of percolated triangulations
Renan Gross, Emmanuel Kammerer, Frederik Ravn Klausen
In this note, using a result of Bernardi, Holden and Sun, we give an explicit geometric relation between the perimeter of the peeling process along the percolation interface of a t…
Polynomial mixing for polygonal side matchings
Renan Gross, Anđela Šarković
We introduce a natural Markov chain on chord diagrams, which, at every step, selects two random chords and swaps them if doing so preserves the diagram's genus. This generalizes th…
Randomly twisted hypercubes -- between structure and randomness
Itai Benjamini, Yotam Dikstein, Renan Gross +1
Twisted hypercubes are generalizations of the Boolean hypercube, obtained by iteratively connecting two instances of a graph by a uniformly random perfect matching. Dudek et al. sh…
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…
Decomposition of mean-field Gibbs distributions into product measures
Ronen Eldan, Renan Gross
We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose prob…
Exponential random graphs behave like mixtures of stochastic block models
Ronen Eldan, Renan Gross
We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independe…
Indistinguishable sceneries on the Boolean hypercube
Renan Gross, Uri Grupel
We show that the scenery reconstruction problem on the Boolean hypercube is in general impossible. This is done by using locally biased functions, in which every vertex has a const…
Bounding the seed length of Miller and Shi's unbounded randomness expansion protocol
Renan Gross, Scott Aaronson
Recent randomness expansion protocols have been proposed which are able to generate an unbounded amount of randomness from a finite amount of truly random initial seed. One such pr…