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math.CO2022
Isoperimetric Inequalities Made Simpler
Ronen Eldan, Guy Kindler, Noam Lifshitz +1
We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show: 1. An elementary proof of classical isoperimetric inequalities…
math.CO2019
Second-order bounds on correlations between increasing families
Ronen Eldan
Harris's correlation inequality states that any two monotone functions on the Boolean hypercube are positively correlated. Talagrand \cite{Talcorr} started a line of works in searc…
math.CO2015★ 1 cited
Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors
Ronen Eldan, Miklós Rácz, Tselil Schramm
We study how the spectral gap of the normalized Laplacian of a random graph changes when an edge is added to or removed from the graph. There are known examples of graphs where, pe…