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Large deviations for voter model occupation times in two dimensions

G. Maillard, T. Mountford (2009)

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

We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model η: ℤ2×[0, ∞)→{0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density ρ∈(0, 1). In [Probab. Theory Related Fields77 (1988) 401–413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log2(t)]. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are log2(t) when...

Large scale behavior of semiflexible heteropolymers

Francesco Caravenna, Giambattista Giacomin, Massimiliano Gubinelli (2010)

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

We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...

Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case

Michael M. Erlihson, Boris L. Granovsky (2008)

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

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...

Limit theorems for the painting of graphs by clusters

Olivier Garet (2001)

ESAIM: Probability and Statistics

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 the Central...

Limit Theorems for the painting of graphs by clusters

Olivier Garet (2010)

ESAIM: Probability and Statistics

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 the Central Limit...

Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope f r c of a given function f : ℝ n × m → ℝ , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A linearly convergent iterative algorithm that approximates the rank-1 convex envelope  f r c of a given function f : ℝ n × m → ℝ , i.e. the largest function below f which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

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