most citedA probabilistic approach to the geometry of the \ell_p^n-ball

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math.PR2005181 cited

A probabilistic approach to the geometry of the \ell_p^n-ball

Franck Barthe, Olivier Guedon, Shahar Mendelson +1

This article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms of independent random variabl…

math.PR2004

Coin flipping from a cosmic source: On error correction of truly random bits

Elchanan Mossel, Ryan O'Donnell

We study a problem related to coin flipping, coding theory, and noise sensitivity. Consider a source of truly random bits $x \in \bits^n$, and parties, who have noisy versions…

math.PR20045 cited

Uniqueness of maximal entropy measure on essential spanning forests

Scott Sheffield

An essential spanning forest of an infinite graph is a spanning forest of in which all trees have infinitely many vertices. Let be an increasing sequence of finite co…

math.PR20043 cited

Random subgraphs of finite graphs: III. The phase transition for the -cube

Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2

We study random subgraphs of the -cube , where nearest-neighbor edges are occupied with probability . Let be the value of for which the expected clust…

math.PR2004

Random subgraphs of finite graphs: II. The lace expansion and the triangle condition

Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2

In a previous paper, we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph, and sh…

math.PR200489 cited

Random subgraphs of finite graphs: I. The scaling window under the triangle condition

Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2

We study random subgraphs of an arbitrary finite connected transitive graph obtained by independently deleting edges with probability . Let be the number of ve…