WebOn the other hand, harmonic measures arising from random walks. We prove that the absolute continuity between a harmonic measure and a Gibbs measure is equivalent to a relation between entropy, drift and critical exponent, extending the previous “fundamental inequality” of Guivarc’h, Ledrappier, and Blachere-Haissinsky-Mathieu. WebAug 25, 2024 · Mathieu “ Asymptotic entropy and green speed for random walks on countable groups ...
arXiv:1708.02133v3 [math.GR] 5 Dec 2024
WebWe are interested in the Guivarc’h inequality for admissible random walks on finitely generated relatively hyperbolic groups, endowed with a word metric. We show that for … WebFeb 17, 2024 · The ideal boundary of a negatively curved manifold naturally carries two types of measures. On the one hand, we have conditionals for equilibrium (Gibbs) states associated to Hoelder potentials; these include the Patterson-Sullivan measure and the Liouville measure. photograph of queen victoria
Entropy and Drift for Random Walks on Negatively Curved Manifolds
WebAt first sight, Theorem 1.5 seems to be the most delicate (this is the only one with the assumption that Γ is not virtually free). However, this is also the setting that has been mostly studied in the literature. Hence, we may use several known results, including most notably results of Ancona [ancona], of Blachère, Haïssinsky and Mathieu [BHM_2] and Tanaka … WebSebastien Blachere. Internal Diffusion Limited Aggregation is a growth model on an infinite set G, associated to a Markov chain on G. It has been introduced by Diaconis and Fulton in 1991 (Rend ... WebSecond, we show that the absolute continuity between a harmonic measure and a Gibbs measure is equivalent to a relation between entropy, (generalized) drift and critical … how does the united nations prevent wars