The Ratio Set of the Harmonic Measure of a Random Walk on a Hyperbolic Group
نویسندگان
چکیده
We consider the harmonic measure on the Gromov boundary of a nonamenable hyperbolic group defined by a finite range random walk on the group, and study the corresponding orbit equivalence relation on the boundary. It is known to be always amenable and of type III. We determine its ratio set by showing that it is generated by certain values of the Martin kernel. In particular, we show that the equivalence relation is never of type III0.
منابع مشابه
Strong Hyperbolicity
We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with sharp additional properties. Specifically, strongly hyperbolic spaces are Gromov hyperbolic spaces that are metrically well-behaved at infinity, and, under weak geodesic assumptions, they are strongly bolic as well. We show that CAT(−1) spaces are strongly hyperbolic. On the way, we determine the best ...
متن کاملTesting Weak-Form Efficient Capital Market Case Study: TSE and DJUS Indices
The present study investigated weak-form market information efficiency in Tehran security exchange (TSE) as an emerging market and in Dow Jones United States security exchange (DJUS) as a developed market based on random walk model. In each market, the random walk model was examined using daily and monthly returns of a set of indices. The results of the parametric and non-parametric tests indic...
متن کاملOn characterizations of hyperbolic harmonic Bloch and Besov spaces
We define hyperbolic harmonic $omega$-$alpha$-Bloch space $mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and characterize it in terms of $$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}},$$ where $0leq gammaleq 1$. Similar results are extended to little $omega$-$alpha$-Bloch and Besov spaces. These obtained...
متن کاملRandom Heegaard splittings
Consider a random walk on the mapping class group, and let wn be the location of the random walk at time n. A random Heegaard splitting M(wn) is a 3-manifold obtained by using wn as the gluing map between two handlebodies. We show that the joint distribution of (wn, w −1 n ) is asymptotically independent, and converges to the product of the harmonic and reflected harmonic measures defined by th...
متن کاملA Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index
Study of volatility has been considered by the academics and decision makers dur-ing two last decades. First since the volatility has been a risk criterion it has been used by many decision makers and activists in capital market. Over the years it has been of more importance because of the effect of volatility on economy and capital markets stability for stocks, bonds, and foreign exchange mark...
متن کامل