The Poisson Boundary of Polycyclic Groups

نویسنده

  • Vadim A. KAIMANOVICH
چکیده

The Poisson boundary for measures with a nite rst moment on polycyclic groups is shown to coincide with the corresponding contracting nilpotent Lie group. The proof is based on using a geometric \strip criterion" of boundary maximality due to the author and a simple estimate of the \neutral component" of the random walk.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Poisson Formula for Groups with Hyperbolic Properties

The Poisson boundary of a group G with a probability measure μ on it is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an integral representation of bounded μ-harmonic functions on G. In this paper we develop a new method of identifying the Poisson boundary based on entropy estimat...

متن کامل

Risk of Sequential Estimator of the Failure Rate of Exponential Distribution under Convex Boundary

In this paper the exact determination of the distribution of stopping variable, the moment and risk of sequential estimator of the failure rate of exponential distribution, under convex boundary is obtained. The corresponding Poisson Process is used to derive the exact distribution of stopping variable of sequential estimator of the failure rate. In the end the exact values of mean and risk ...

متن کامل

A note on the Poisson boundary of lamplighter random walks

The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups Γ endowed with a “rich” boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich [16]. A geometrical method for constructing the strip as a subset of the lamplighter group ...

متن کامل

Harmonic Functions on Discrete Subgroups of Semi - Simple Lie Groups

A description of the Poisson boundary of random walks on discrete subgroups of semi-simple Lie groups in terms of geometric boundaries of the corresponding Riemannian symmetric spaces is given. Let G be a discrete group, and { a probability measure on G. A function f on G is called-harmonic if f(g) = P f(gx) (x) 8 g 2 G. The Poisson boundary of the pair (G;) is the probability space (?;) with a...

متن کامل

Electrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory

Electrostatic potential as well as the local volume charge density are computed for a macromolecule by solving the Poisson-Boltzmann equation (PBE) using the finite element method (FEM). As a verification, our numerical results for a one dimensional PBE, which corresponds to an infinite-length macromolecule, are compared with the existing analytical solution and good agreement is found. As a ma...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007