All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 64

Showing per page

Scale-free percolation

Maria Deijfen, Remco van der Hofstad, Gerard Hooghiemstra (2013)

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

We formulate and study a model for inhomogeneous long-range percolation on ℤ d . Each vertex x ∈ ℤ d is assigned a non-negative weight W x , where ( W x ) x ∈ ℤ d are i.i.d. random variables. Conditionally on the weights, and given two parameters α , λ g t ; 0 , the edges are independent and the probability that there is an edge between x and y is given by p x y = 1 - exp { - λ W x W y / | x - y | α } . The parameter λ is the percolation parameter, while α describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether there...

Scaling limit and cube-root fluctuations in SOS surfaces above a wall

Pietro Caputo, Eyal Lubetzky, Fabio Martinelli, Allan Sly, Fabio Lucio Toninelli (2016)

Journal of the European Mathematical Society

Consider the classical ( 2 + 1 ) -dimensional Solid-On-Solid model above a hard wall on an L × L box of ℤ 2 . The model describes a crystal surface by assigning a non-negative integer height η x to each site x in the box and 0 heights to its boundary. The probability of a surface configuration η is proportional to exp ( - β ℋ ( η ) ) , where β is the inverse-temperature and ℋ ( η ) sums the absolute values of height differences between neighboring sites. We give a full description of the shape of the SOS surface for low enough temperatures....

Scaling limits of anisotropic Hastings–Levitov clusters

Fredrik Johansson Viklund, Alan Sola, Amanda Turner (2012)

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

We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations...

Scaling of a random walk on a supercritical contact process

F. den Hollander, R. S. dos Santos (2014)

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

We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...

Shape transition under excess self-intersections for transient random walk

Amine Asselah (2010)

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

We reveal a shape transition for a transient simple random walk forced to realize an excess q-norm of the local times, as the parameter q crosses the value qc(d)=d/(d−2). Also, as an application of our approach, we establish a central limit theorem for the q-norm of the local times in dimension 4 or more.

SLE and triangles.

Dubédat, Julien (2003)

Electronic Communications in Probability [electronic only]

SLE et invariance conforme

Jean Bertoin (2003/2004)

Séminaire Bourbaki

Les processus de Schramm-Loewner (SLE) induisent des courbes aléatoires du plan complexe, qui vérifient une propriété d’invariance conforme. Ce sont des outils fondamentaux pour la compréhension du comportement asymptotique en régime critique de certains modèles discrets intervenant en physique statistique ; ils ont permis notamment d’établir rigoureusement certaines conjectures importantes dans ce domaine.

Small-time behavior of beta coalescents

Julien Berestycki, Nathanaël Berestycki, Jason Schweinsberg (2008)

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

For a finite measure Λ on [0, 1], the Λ-coalescent is a coalescent process such that, whenever there are b clusters, each k-tuple of clusters merges into one at rate ∫01xk−2(1−x)b−kΛ(dx). It has recently been shown that if 1<α<2, the Λ-coalescent in which Λ is the Beta (2−α, α) distribution can be used to describe the genealogy of a continuous-state branching process (CSBP) with an α-stable branching mechanism. Here we use facts about CSBPs to establish new results about the small-time...

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

In this paper we establish a decoupling feature of the random interlacement process ℐ u ⊂ ℤ d at level u , d ≥ 3 . Roughly speaking, we show that observations of ℐ u restricted to two disjoint subsets A 1 and A 2 of ℤ d are approximately independent, once we add a sprinkling to the process ℐ u by slightly increasing the parameter u . Our results differ from previous ones in that we allow the mutual distance between the sets A 1 and A 2 to be much smaller than their diameters. We then provide an important application of this...

Currently displaying 1 – 20 of 64

Page 1 Next