Related papers: Gibbs measures for geodesic flow on CAT(-1) spaces

This monograph resolves - in a dense class of cases - several open problems concerning geodesics in i.i.d. first-passage percolation on $\mathbb{Z}^d$. Our primary interest is in the empirical measures of edge-weights observed along…

For any non-elementary, torsion-free hyperbolic group, we provide a correspondence between the left-invariant Gromov-hyperbolic metrics on the group that are quasi-isometric to a word metric, and continuous reparameterizations of the…

A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two points can be defined as the amount of probability mass accumulated…

We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is…

We prove that an IRS of a group with a geometrically dense action on a CAT(0) space also acts geometrically densely; assuming the space is either of finite telescopic dimension or locally compact with finite dimensional Tits boundary. This…

We prove that there is only one translation-invariant Gibbsian point process w.r.t. to a chosen interaction if any of them satisfies a certain bound related to concentration-of-measure. This concentration-of-measure bound is e.g. fulfilled…

In a recent paper, in collaboration with Mathieu Lewin and Phan Th{\`a}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This…

Equilibrium states for geodesic flows over closed rank 1 manifolds were studied recently by Burns, Climenhaga, Fisher and Thompson. For sufficiently regular potentials, it was shown that if the singular set does not carry full pressure then…

We assume one site measures without a boundary $e^{-\phi(x)}dx/Z$ that satisfy a log-Sobolev inequality. We prove that if these measures are perturbed with quadratic interactions, then the associated infinite dimensional Gibbs measure on…

Let $M=X/\Gamma$ be a geometrically finite negatively curved manifold with fundamental group $\Gamma$ acting on $X$ by isometries. The purpose of this paper is to study the mixing property of the geodesic flow on $T^1M$, the asymptotic…

It is well known that the Gibbs inequality, which says that the Gibbs ratio is bounded above and below by positive constants, holds for the unique equilibrium states of H\"older continuous potentials on shift spaces, but it can fail for…

For a geodesic ball with non-negative Ricci curvature and almost maximal volume, without using compactness argument, we construct an $\epsilon$-splitting map on a concentric geodesic ball with uniformly small radius. There are two new…

This work presents an explicit description of the Fisher-Rao Riemannian metric on the Hilbert manifold of equivalent centered Gaussian measures on an infinite-dimensional Hilbert space. We show that the corresponding quantities from the…

The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy momentum tensor in Universes with non trivial topology. The purpose of this work is to…

We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…

We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for H\"older potentials satisfying the pressure gap condition. In addition, we provide a criterion for a continuous potential to satisfy the…

We prove a version of the Hopf-Rinow-theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essential local…

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…

We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…

Consider a H\"older continuous potential $\phi$ defined on the full shift $A^\nn$, where $A$ is a finite alphabet. Let $X\subset A^\nn$ be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$…