Communications in Mathematical Physics - Volume 236 by M. Aizenman (Chief Editor)

By M. Aizenman (Chief Editor)

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Bounds for |u| 1. As was the case for the resolvent, we have to identify more precisely the leading term of the inhomogeneous term for the contribution to the inversion integral for u very close to the origin. 153). 21. 9), P τTσ(E)\σ > m, σ (m) = σ − pN (σ, σ )m ≤ Cme−β √ NEσ −m/EτTσ (E)\σ bσ e . 155) 44 G. Ben Arous, A. Bovier, V. Gayrard Proof. Note that pN (σ, σ )m is the probability of the event that σ (k) remains at σ during the entire period from time zero to time m which is a subset of the event {τTσ(E)\σ > m, σ (m) = σ }.

108, 225–239 (1987) Communicated by M. Aizenman Commun. Math. Phys. 1007/s00220-003-0803-y Communications in Mathematical Physics Thermodynamical Limit for Correlated Gaussian Random Energy Models P. Contucci, M. Degli Esposti, C. Giardin`a, S. Graffi Dipartimento di Matematica, Universit`a di Bologna, 40127 Bologna, Italy. it Received: 17 June 2002 / Accepted: 31 October 2002 Published online: 21 February 2003 – © Springer-Verlag 2003 To Francesco Guerra on his sixtieth birthday Abstract: Let {Eσ (N )}σ ∈ N be a family of | N | = 2N centered unit Gaussian random variables defined√ by the covariance matrix CN of elements cN (σ, τ ) :=Av(Eσ (N )Eτ (N )) and HN (σ ) = − N Eσ (N ) the corresponding random Hamiltonian.

Derrida’s generalized random energy models. 1. Poisson cascades and extremal processes. Preprint 727, U. : Random energy model: limit of a family of disordered system. Phys. Rev. Lett. : Random energy model: an exactly solvable model of disordered system. Phys. Rev. : Solution of the generalised random energy model. Phys. : The thermodynamical limit in mean field spin glass model. Commun. Math. Phys. : Une inegalite du type de Slepian et Gordon sur les processus gaussiens. Israel J. Math. : Probability on Banach spaces.

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