ar X iv : m at h / 06 11 72 1 v 1 [ m at h . PR ] 2 3 N ov 2 00 6 A LATTICE GAS MODEL FOR THE INCOMPRESSIBLE NAVIER - STOKES EQUATION

ar X iv : m at h / 05 05 09 0 v 1 [ m at h . PR ] 5 M ay 2 00 5 SUPERDIFFUSIVITY OF TWO DIMENSIONAL LATTICE GAS MODELS

It was proved [4, 13] that stochastic lattice gas dynamics converge to the Navier-Stokes equations in dimension d = 3 in the incompressible limits. In particular, the viscosity is finite. We proved that, on the other hand, the viscosity for a two dimensional lattice gas model diverges faster than log log t. Our argument indicates that the correct divergence rate is (log t) 1/2. This problem is ...

ar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

ar X iv : m at h / 06 11 45 2 v 1 [ m at h . A G ] 1 5 N ov 2 00 6 UNIRATIONALITY OF CERTAIN SUPERSINGULAR K 3 SURFACES IN CHARACTERISTIC

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

ar X iv : h ep - l at / 0 11 00 06 v 3 6 N ov 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 06 11 11 6 v 1 [ m at h . PR ] 5 N ov 2 00 6 SLE 6 and CLE 6 from Critical Percolation ∗

We review some of the recent progress on the scaling limit of two-dimensional critical percolation; in particular, the convergence of the exploration path to chordal SLE6 and the “full” scaling limit of cluster interface loops. The results given here on the full scaling limit and its conformal invariance extend those presented previously. For site percolation on the triangular lattice, the resu...