Longest increasing subsequences of random colored permutations.
Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients
Loop-free Markov chains as determinantal point processes
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
Lower deviation probabilities for supercritical Galton–Watson processes
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.
Lyapunov exponents for the one-dimensional parabolic Anderson model with drift.
Lyapunov exponents of linear stochastic functional differential equations driven by semimartingales. Part I : the multiplicative ergodic theory