Displaying similar documents to “Percolation transition for some excursion sets.”

Eigenvalues of GUE minors.

Johansson, Kurt, Nordenstam, Eric (2006)

Electronic Journal of Probability [electronic only]

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A strong invariance principle for negatively associated random fields

Guang-hui Cai (2011)

Czechoslovak Mathematical Journal

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In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite ( 2 + δ ) th moment and the covariance coefficient u ( n ) exponentially decreases to 0 . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.

Limit theorems for the painting of graphs by clusters

Olivier Garet (2001)

ESAIM: Probability and Statistics

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We consider a generalization of the so-called divide and color model recently introduced by Häggström. We investigate the behavior of the magnetization in large boxes of the lattice ℤ d and its fluctuations. Thus, Laws of Large Numbers and Central Limit Theorems are proved, both quenched and annealed. We show that the properties of the underlying percolation process deeply influence the behavior of the coloring model. In the subcritical case, the limit magnetization is deterministic and...

On the proof of the Parisi formula by Guerra and Talagrand

Erwin Bolthausen (2004-2005)

Séminaire Bourbaki

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The Parisi formula is an expression for the limiting free energy of the Sherrington-Kirkpatrick spin glass model, which had first been derived by Parisi using a non-rigorous replica method together with an hierarchical ansatz for the solution of the variational problem. It had become quickly clear that behind the solution, if correct, lies an interesting mathematical structure. The formula has recently been proved by Michel Talagrand based partly on earlier ideas and results by Francesco...