A note on Talagrand's positivity principle.

Panchenko, Dmitriy

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On the proof of the Parisi formula by Guerra and Talagrand

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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...

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The realization of positive random variables via absolutely continuous transformations of measure on Wiener space.

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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...

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The Barnes G function and its relations with sums and products of generalized gamma convolution variables.

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On differentiability of the Parisi formula.

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On the bounded laws of iterated logarithm in Banach space

Dianliang Deng (2005)

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In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.