Related papers: Entropy Rigidity for Maximal Representations

Let $\Gamma_1$ and $\Gamma_2$ be two lattices of finite covolume in a semisimple Lie group $G$. We prove a spectral rigidity result for the representation spectra of the right regular representations $L^2(\Gamma_1 \backslash G)$ and…

Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations,…

Let $\Gamma$ be a relatively hyperbolic group and let $\mu$ be an admissible symmetric finitely supported probability measure on $\Gamma$. We extend Floyd-Ancona type inequalities up to the spectral radius of $\mu$. We then show that when…

Generalizing results of Deroin-Dujardin, we introduce the notion of proximal stability for a holomorphic family $ (\rho_{\lambda}) $ of representations $ \Gamma \to \text{SL}(d, \mathbb{C}) $, where $ \Gamma $ is a finitely generated group,…

Fix n>2. Let s be a principally embedded sl(2)-subalgebra in sl(n). A special case of results of the second author and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite dimensional…

Let $\rho\colon G\to \mathrm{GL}_n(K)$ be an continuous irreducible representation of a compact group over a complete discretely valued field $K$. Let $W_i,W_j$ be two irreducible subrepresentations of $\overline{\rho}^{ss}$, the…

In this paper we establish a dichotomy for the ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with one-dimensional compact center leaves which are virtually skew products over (transitive) Anosov homeomorphism.…

We study the limit of large volume equilibrium Gibbs measures for a rather general Hamiltonians. In particular we study Hamiltonians which arise in naturally in Nonlinear Elasticity and Hamiltonians (containing surface terms) which arises…

In this paper we prove the following theorem. Let L/\Q_p be a finite extension with ring of integers O_L and maximal ideal lambda. Theorem 1. Suppose that p >= 5. Suppose also that \rho:G_\Q -> GL_2(O_L) is a continuous representation…

We prove a finite smooth version of the entropic continuity of Lyapunov exponents of Buzzi-Crovisier-Sarig for $C^\infty$ surface diffeomorphisms [9]. As a consequence we show that any $C^r$, $r > 1$, smooth surface diffeomorphism $f$ with…

Let $G$ be a connected semisimple real algebraic group and $\Gamma<G$ be its Zariski dense discrete subgroup. We prove that if $\Gamma\backslash G$ admits any finite Bowen-Margulis-Sullivan measure, then $\Gamma$ is virtually a product of…

Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group $SL(d+1,\C)$. Both are obtained from the K\"ahler potential of the underlying geometry of the sphere corresponding to the…

Let $\Gamma$ be an irreducible lattice in a semisimple Lie group of real rank at least $2$. Suppose that $\Gamma$ has property (T;FD), that is, its finite dimensional representations have a uniform spectral gap. We show that if $\Gamma$ is…

Let $\Gamma$ denote a lattice in $SU(1,p)$, with $p$ greater than 1. We show that there exists no Zariski dense maximal representation with target $SU(m,n)$ if $n>m>1$. The proof is geometric and is based on the study of the rigidity…

For any rank-one convex projective manifold with a compact convex core, we prove that there exists a unique probability measure of maximal entropy on the set of unit tangent vectors whose geodesic is contained in the convex core, and that…

We single out a large class of groups ${\mathscr{M}}$ for which the following unique prime factorization result holds: if $\Gamma_1,\dots,\Gamma_n\in {\mathscr{M}}$ and $\Gamma_1\times\dots\times\Gamma_n$ is measure equivalent to a product…

Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…

We study the maximal perimeter constant of isotropic log-concave probability measures on $\mathbb{R}^n$. For a measure $\mu$, this quantity, denoted by $\Gamma(\mu)$, is defined as the supremum of the $\mu$-perimeter over all convex bodies…

Given an Anosov representation $\rho \colon \pi_1(S) \to \PSL_{n}(\mathbb{R})$ and a maximal geodesic lamination $\lambda$ in a surface $S$, we construct shear deformations along the leaves of the geodesic lamination $\lambda$ endowed with…

Let S be a principally embedded sl_2 subalgebra in sl_n for n > 2. A special case of results of the third author and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite-dimensional irreducible sl_n…