Non - Liouville groups with return probability exponent at most 1 / 2
نویسندگان
چکیده
We construct a finitely generated group G without the Liouville property such that the return probability of a random walk satisfies p2n(e, e) & e−n 1/2+o(1) . This shows that the constant 1/2 in a recent theorem by Saloff-Coste and Zheng, saying that return probability exponent less than 1/2 implies the Liouville property, cannot be improved. Our construction is based on permutational wreath products over tree-like Schreier graphs and the analysis of large deviations of inverted orbits on such graphs.
منابع مشابه
Non-perturbative Solution of Matrix Models Modified by Trace-squared Terms
We present a non-perturbative solution of large N matrix models modified by terms of the form g(TrΦ4)2, which add microscopic wormholes to the random surface geometry. For g < gt the sum over surfaces is in the same universality class as the g = 0 theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction ∼ eα+φ. For g = gt we find a different univers...
متن کاملCopolymers at Selective Interfaces: New Bounds on the Phase Diagram
We investigate the phase diagram of disordered copolymers at the interface between two selective solvents, and in particular its weak-coupling behavior, encoded in the slope mc of the critical line at the origin. We focus on the directed walk case, which has turned out to be, in spite of the apparent simplicity, extremely challenging. In mathematical terms, the partition function of such a mode...
متن کاملInfinite ergodic theory for Kleinian groups
In this paper we use infinite ergodic theory to study limit sets of essentially free Kleinian groups which may have parabolic elements of arbitrary rank. By adapting a method of Adler, we construct a section map S for the geodesic flow on the associated hyperbolic manifold. We then show that this map has the Markov property and that it is conservative and ergodic with respect to the invariant m...
متن کاملTouching random surfaces and Liouville gravity.
Large N matrix models modified by terms of the form g(TrΦn)2 generate random surfaces which touch at isolated points. Matrix model results indicate that, as g is increased to a special value gt, the string susceptibility exponent suddenly jumps from its conventional value γ to γ γ−1 . We study this effect in Liouville gravity and attribute it to a change of the interaction term from Oeα+φ for g...
متن کاملPreferential Behaviour and Scaling in Diffusive Dynamics on Networks
We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges. Scaling in the fluctuations occurs when the dispersion of a quantity at each node or edge increases like the its mean to the power μ. We show that the occurrence ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015