Periodic Schur process is a generalization of the Schur process introduced in [OR1]. We compute its correlation functions and their bulk scaling limits, and we discuss several applications, including asymptotic analysis of uniform measures on cylindric partitions, time-dependent extensions of the discrete sine kernel, and bulk limit behavior of certain measures on partitions introduced in [NO] in connection with supersymmetric gauge theories

We prove that the integrated density of states (IDS) of random Schrödinger operators with Anderson-type potentials on $L^2({\mathbb{R}}^d)$ for $d\ge 1$ is locally Hölder continuous at all energies with the same Hölder exponent $0<\alpha \le 1$ as the conditional probability measure for the single-site random variable. As a special case, we prove that if the probability distribution is absolutely continuous with respect to Lebesgue measure with a bounded density, then the IDS is Lipschitz continuous at all energies. The single-site potential $u\in L_0^{\infty }({\mathbb{R}}^d)$ must be nonnegative and compactly supported. The unperturbed Hamiltonian must be periodic and satisfy a unique continuation principle (UCP). We also prove analogous continuity results for the IDS of random Anderson-type perturbations of the Landau Hamiltonian in two dimensions. All of these results follow from a new Wegner estimate for local random Hamiltonians with rather general probability measures

L'un des buts de cet article est de décrire l'isomorphisme entre les tours de Lubin-Tate et de Drinfeld au niveau de leurs squelettes après quotient par ${\text{GL}}_n(O_F)\times O_D^{\times }$ ou bien $I\times O_D^{\times }$, où $O_D$ est l'ordre maximal dans l'algèbre à division d'invariant $1/n$ sur $F$ et $I$ un sous-groupe d'Iwahori de ${\text{GL}}_n$. Nous donnons des applications à l'étude des sous-groupes canoniques sur les espaces de Lubin-Tate, la description des orbites de Hecke sphériques dans ces espaces, les domaines fondamentaux pour les correspondances de Hecke et l'application des périodes de Gross-Hopkins. Nous-y étudions également en détail les filtrations de ramification (inférieure et supérieure) et l'application de Hodge-Tate d'un groupe formel $p$-divisible de dimension un.

One of the goals of this article is to describe the isomorphism between Lubin-Tate and Drinfeld towers at the level of their skeletons after taking quotient by ${\text{GL}}_n(O_F)\times O_D^{\times }$ or $I\times O_D^{\times }$, where $O_D$ is the maximal order in the division algebra with invariant $1/n$ over $F$ and $I$ an Iwahori subgroup of ${\text{GL}}_n$. We give applications to the theory of canonical subgroups on Lubin-Tate spaces, the description of spherical Hecke orbits in those spaces, fundamental domains for Hecke correspondences, and the Gross-Hopkins period mapping. We also study in detail the ramification filtrations (upper and lower) and the Hodge-Tate map of a one-dimensional formal $p$-divisible group

We prove that steady periodic two-dimensional rotational gravity water waves with a monotone surface profile between troughs and crests have to be symmetric about the crest, irrespective of the vorticity distribution within the fluid