Displaying similar documents to “Limiting curlicue measures for theta sums”

Planar Lorentz process in a random scenery

Françoise Pène (2009)

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

Similarity:

We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by...

Copolymer at selective interfaces and pinning potentials : weak coupling limits

Nicolas Petrelis (2009)

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

Similarity:

We consider a simple random walk of length , denoted by ( ), and we define ( ) a sequence of centered i.i.d. random variables. For ∈ℕ we define (( , …, )) an i.i.d sequence of random vectors. We set ∈ℝ, ≥0 and ≥0, and transform the measure on the set of random walk trajectories with the hamiltonian ∑ ( +)sign( )+∑ ∑ ...

Disorder relevance for the random walk pinning model in dimension 3

Matthias Birkner, Rongfeng Sun (2011)

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

Similarity:

We study the continuous time version of the , where conditioned on a continuous time random walk ( )≥0 on ℤ with jump rate > 0, which plays the role of disorder, the law up to time of a second independent random walk ( )0≤≤ with jump rate 1 is Gibbs transformed with weight e (,), where (, ) is the collision local time between and up to time . As the inverse temperature varies, the model undergoes a localization–delocalization...

Exponential concentration for first passage percolation through modified Poincaré inequalities

Michel Benaïm, Raphaël Rossignol (2008)

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

Similarity:

We provide a new exponential concentration inequality for first passage percolation valid for a wide class of edge times distributions. This improves and extends a result by Benjamini, Kalai and Schramm ( (2003)) which gave a variance bound for Bernoulli edge times. Our approach is based on some functional inequalities extending the work of Rossignol ( (2006)), Falik and Samorodnitsky ( (2007)).

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

Similarity:

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ∼ , →∞, >0, where 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...