Limit laws for a coagulation model of interacting random particles
Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case
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 random fields [Book]
Limit theorems for the painting of graphs by clusters
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 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
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 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...
Limit theorems for vertex-reinforced jump processes on regular trees.
Limit velocity for a driven particle in a random medium with mass aggregation
Limits of determinantal processes near a tacnode
We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter ε > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process....
Linear speed large deviations for percolation clusters.
Lipschitz percolation.
Local bootstrap percolation.
Local energy statistics in directed polymers.
Local percolative properties of the vacant set of random interlacements with small intensity
Random interlacements at level is a one parameter family of connected random subsets of , (Ann. Math.171(2010) 2039–2087). Its complement, the vacant set at level , exhibits a non-trivial percolation phase transition in (Comm. Pure Appl. Math.62 (2009) 831–858; Ann. Math.171 (2010) 2039–2087), and the infinite connected component, when it exists, is almost surely unique (Ann. Appl. Probab.19(2009) 454–466). In this paper we study local percolative properties of the vacant set of random interlacements...
Local sub-Gaussian estimates on graphs: The strongly recurrent case.
Localization and delocalization of random interfaces.
Logarithmic components of the vacant set for random walk on a discrete torus.
Logarithmic Sobolev inequalities for unbounded spin systems revisited
Logarithmic Sobolev inequality for zero-range dynamics: independence of the number of particles.
Lower large deviations and laws of large numbers for maximal flows through a box in first passage percolation
We consider the standard first passage percolation model in ℤd for d≥2. We are interested in two quantities, the maximal flow τ between the lower half and the upper half of the box, and the maximal flow ϕ between the top and the bottom of the box. A standard subadditive argument yields the law of large numbers for τ in rational directions. Kesten and Zhang have proved the law of large numbers for τ and ϕ when the sides of the box are parallel to the coordinate hyperplanes: the two variables grow...
Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation
Equip the edges of the lattice ℤ2 with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in ℝ2 when the side lengths of the rectangle go to infinity. We prove that the lower large deviations are of surface order, and we prove the corresponding large deviation principle from below. This extends and improves previous large deviations results of Grimmett and Kesten [9] obtained for boxes of particular orientation.