Related papers: Patterson-Sullivan theory for groups with a strong…

Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…

We define a new notion of contracting element of a group and we show that contracting elements coincide with hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, rank one isometries in groups acting…

We present a survey of results related to the Milnor's problem on group growth. We discuss the cases of polynomial growth, exponential but not uniformly exponential growth, but the main part of the article is devoted to the intermediate…

Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements 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)…

Thurston proposed, in part of an unfinished manuscript, to study surface group actions on $S^1$ by using an $S^1$-connection on the suspension bundle obtained from a harmonic measure. Following the approach and previous work of the authors,…

We address the following natural extension problem for group actions: Given a group $G$, a subgroup $H\le G$, and an action of $H$ on a metric space, when is it possible to extend it to an action of the whole group $G$ on a (possibly…

Consider the geodesic flow on a closed rank one manifold of nonpositive curvature. For certain H\"{o}lder continuous potential, there exists a unique equilibrium state by \cite{BCFT}. In this paper, we introduce the notions of core limit…

Let $\Gamma$ be a Gromov hyperbolic group, endowed with an arbitrary left-invariant hyperbolic metric, quasi-isometric to a word metric. The action of $\Gamma$ on its boundary $\partial\Gamma$ endowed with the Patterson-Sullivan measure…

We consider the approximation of Poisson type problems where the source is given by a singular measure and the domain is a convex polygonal or polyhedral domain. First, we prove the well-posedness of the Poisson problem when the source…

We formulate Poisson Chern-Simons gauge theories on compact group manifolds. These describe a sector of the large representation limit of noncommutative Chern-Simons in the same way as the light-cone formulation of the membrane action…

We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $\Psi$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded,..., and show how these notions behave according to the growth of…

In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of…

In this paper we study the Hutchinson-Barnsley theory of fractals in the setting of multimetric spaces (which are sets endowed with point separating families of pseudometrics) and in the setting of topological spaces. We find natural…

We extend several notions and results from the classical Patterson-Sullivan theory to the setting of Anosov subgroups of higher rank semisimple Lie groups, working primarily with invariant Finsler metrics on associated symmetric spaces. In…

When multitudes of features can plausibly be associated with a response, both privacy considerations and model parsimony suggest grouping them to increase the predictive power of a regression model. Specifically, the identification of…

We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…

In the high temperature phase of Yang-Mills theories, large spatial Wilson loops show area law behaviour with a string tension that grows with increasing temperature. Within the framework of the commonly used string picture we use a large…

Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…

The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…