Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Gross, Renan"'
Let $S$ be a compact hyperbolic surface of genus $g\geq 2$ and let $I(S) = \frac{1}{\mathrm{Vol}(S)}\int_{S} \frac{1}{\mathrm{Inj}(x)^2 \wedge 1} dx$, where $\mathrm{Inj}(x)$ is the injectivity radius at $x$. We prove that for any $k\in \{1,\ldots, 2
Externí odkaz:
http://arxiv.org/abs/2407.21780
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. showed that when the two instances are independent, these graphs have op
Externí odkaz:
http://arxiv.org/abs/2211.06988
Autor:
Gross, Renan
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 that the limiting run-time complexity of a natural class of these alg
Externí odkaz:
http://arxiv.org/abs/2201.10350
Autor:
Gross, Renan
We study the scenery reconstruction problem on the $d$-dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right dr
Externí odkaz:
http://arxiv.org/abs/2011.14153
Autor:
Be`er, Avraham, Ilkanaiv, Bella, Gross, Renan, Kearns, Daniel B., Heidenreich, Sebastian, Bär, Markus, Ariel, Gil
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 that use energy to generate motion. Accordingly, understanding the cons
Externí odkaz:
http://arxiv.org/abs/1911.05434
Autor:
Eldan, Ronen, Gross, Renan
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 conjecture of Talagrand [Tal97] proving that $$\int_{\left\{ -1,1\right\} ^{
Externí odkaz:
http://arxiv.org/abs/1909.12067
Autor:
Gross, Renan
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 prescribed centered distribution with finite variance. This provides a new, c
Externí odkaz:
http://arxiv.org/abs/1905.00852
Autor:
Eldan, Ronen, Gross, Renan
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 probability vectors are critical points of an associated mean-field functi
Externí odkaz:
http://arxiv.org/abs/1708.05859
Autor:
Eldan, Ronen, Gross, Renan
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 independent edges whose probability matrices are critical points of an associat
Externí odkaz:
http://arxiv.org/abs/1707.01227