Related papers: Stable Random Fields, Patterson-Sullivan measures …

In this paper, we study stable ergodicity of the action of groups of diffeomorphisms on smooth manifolds. Such actions are known to exist only on one-dimensional manifolds. The aim of this paper is to introduce a geometric method to…

Let $G$ be a totally disconnected, locally compact (t.d.l.c.) group. The scale $s_G(g)$ of $g \in G$ in the sense of Willis is given by the minimum value of the index $|gUg^{-1}:U \cap gUg^{-1}|$ as $U$ ranges over the compact open…

This paper deals with measurable stationary symmetric stable random fields indexed by R^d and their relationship with the ergodic theory of nonsingular R^d-actions. Based on the phenomenal work of Rosinski(2000), we establish extensions of…

This paper presents a study of the asymptotic geometry of groups with contracting elements, with emphasis on a subclass of statistically convex-cocompact (SCC) actions. The class of SCC actions includes relatively hyperbolic groups, CAT(0)…

We focus on two dependency quantities of a max-stable random field $X$ on some space $T$: the extremal coefficient function $\theta$ which we define on finite sets of $T$ and the extremal correlation function $\chi(s,t)=\lim_{x \uparrow…

Consider a free ergodic measure preserving profinite action $\Gamma\curvearrowright X$ (i.e. an inverse limit of actions $\Gamma\curvearrowright X_n$, with $X_n$ finite) of a countable property (T) group $\Gamma$ (more generally of a group…

We consider a finite-dimensional, locally finite CAT(0) cube complex X admitting a co-compact properly discontinuous countable group of automorphisms G. We construct a natural compact metric space B(X) on which G acts by homeomorphisms, the…

We study stationary actions of locally compact measured groups through the structure and regularity of their Radon-Nikodym cocycles. We start with two dynamical consequences of stationarity. Extending a theorem of Furstenberg-Glasner from…

For a given stationary max-stable random field $X(t),t\in Z^d$ the corresponding generalised Pickands constant coincides with the classical extremal index $\theta$ which always exists. In this contribution we discuss necessary and…

We study a notion of deformation for simplicial trees with group actions (G-trees). Here G is a fixed, arbitrary group. Two G-trees are related by a deformation if there is a finite sequence of collapse and expansion moves joining them. We…

We study the asymptotic behaviour of simply connected, Riemannian manifolds $X$ of strictly negative curvature admitting a non-uniform lattice $\Gamma$. If the quotient manifold $\bar X= \Gamma \backslash X$ is asymptotically $1/4$-pinched,…

Field theoretical renormalization group methods are applied to the Obukhov--Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - < v(t,{\bf x}){\bf…

We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0<A_{1}<A_{2}<\cdots $…

We study expansivity and the shadowing property for finitely generated group actions on metric spaces. We consider the projecting and lifting problems for actions having these properties. We prove that every expansive action with the…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…

We prove the existence of extremal, non-csc, K\"ahler metrics on certain unstable projectivised vector bundles $\P (E) \to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic K\"ahler classes. In…

We consider finite 2-complexes X that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT(-1) metrics on X which are piecewise…

In this work the equivariant signature of a manifold with proper action of a discrete group is defined as an invariant of equivariant bordisms. It is shown that the computation of this signature can be reduced to its computation on fixed…

We propose to "gauge" the group of similarity transformations that acts on a space of non-Hermitian scalar theories. We introduce the "similarity gauge field", which acts as a gauge connection on the space of non-Hermitian theories…