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

We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories,…

Fix a finite group $G$. We study $\Omega^{SO,G}_2$ and $\Omega^{U,G}_2$, the unitary and oriented bordism groups of smooth $G$-equivariant compact surfaces, respectively, and we calculate them explicitly. Their ranks are determined by the…

This paper develops graph analogues of the genus bounds for the maximal size of an automorphism group of a compact Riemann surface of genus $g\ge 2$. Inspired by the work of M. Baker and S. Norine on harmonic morphisms between finite…

A group action on a metric space is called growth tight if the exponential growth rate of the group with respect to the induced pseudo-metric is strictly greater than that of its quotients. A prototypical example is the action of a free…

For a non-elementary discrete isometry group $G$ of divergence type acting on a proper geodesic $\delta$-hyperbolic space, we prove that its Patterson measure is quasi-invariant under the normalizer of $G$. As applications of this result,…

This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…

We investigate multidimensional gravity with the Gauss-Bonnet term and with torsion on the space of extra dimensions chosen to be the group manifold of a simple Lie group. We take the Robertson-Walker ansatz for the 4-dimensional space-time…

For a geometrically finite Kleinian group $\Gamma$, the Bowen-Margulis-Sullivan measure is finite and is the unique measure of maximal entropy for the geodesic flow, as shown by Sullivan and Otal-Peign\'e respectively. Moreover, it is…

We extend the notions of topological stability, shadowing and persistence from homeomorphisms to finitely generated group actions on uniform spaces and prove that an expansive action with either shadowing or persistence is topologically…

We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first moment with non-trivial boundary, and show that this…

We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation. Global and local renormalisation group flows are solved analytically in the…

Finding a non-sofic hyperbolic group will resolve two major problems in geometric group theory: Are there non sofic groups? Are there non residually finite hyperbolic groups? In this paper, we propose a new probabilistic approach to this…

A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…

In this paper, we consider the log-concave ensemble of random matrices, a class of covariance-type matrices $XX^*$ with isotropic log-concave $X$-columns. A main example is the covariance estimator of the uniform measure on isotropic convex…

Consider two free measure preserving group actions $\Gamma \actson (X, \mu), \Delta \actson (X, \mu)$, and a measure preserving action $\Delta \actson^a (Z, \nu)$ where $(X, \mu), (Z, \nu)$ are standard probability spaces. We show how to…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

Given a product X of locally compact rank one Hadamard spaces, we study asymptotic properties of certain discrete isometry groups. First we give a detailed description of the structure of the geometric limit set and relate it to the limit…

We study the growth of typical groups from the family of $p$-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound.…

Pseudoscalars appearing in particle physics are reviewd systematically. From the fundamental point of view at an ultra-violat completed theory, they can be light if they are realized as pseudo-Goldstone bosons of some spontaneously broken…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…