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Capacity bounds for the CDMA system and a neural network: a moderate deviations approach

Matthias Löwe, Franck Vermet (2009)

ESAIM: Probability and Statistics

We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values ± 1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari...

Cavity method in the spherical SK model

Dmitry Panchenko (2009)

Annales de l'I.H.P. Probabilités et statistiques

We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford, Li Wu (2008)

Open Mathematics

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than 7 + 41 2 and obeys some natural regularity conditions.

Clusters in middle-phase percolation on hyperbolic plane

Jan Czajkowski (2011)

Banach Center Publications

I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. 0 < p c ( G ) < p u ( G ) < 1 , where p c is the critical probability and p u -the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].

Coexistence probability in the last passage percolation model is 6 - 8 log 2

David Coupier, Philippe Heinrich (2012)

Annales de l'I.H.P. Probabilités et statistiques

A competition model on ℕ 2 between three clusters and governed by directed last passage percolation is considered. We prove that coexistence, i.e. the three clusters are simultaneously unbounded, occurs with probability 6 - 8 log 2 . When this happens, we also prove that the central cluster almost surely has a positive density on ℕ 2 . Our results rely on three couplings, allowing to link the competition interfaces (which represent the borderlines between the clusters) to some particles in the multi-TASEP, and...

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

Pablo A. Ferrari, Patricia Gonçalves, James B. Martin (2009)

Annales de l'I.H.P. Probabilités et statistiques

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p∈(1/2, 1] and to the left at rate 1−p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the...

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