Decomposition of random walk measures on the one-dimensional torus.

  title={Decomposition of random walk measures on the one-dimensional torus.},
  author={Tom Gilat},
  journal={discrete Analysis},
  • T. Gilat
  • Published 15 September 2019
  • Mathematics
  • discrete Analysis
The main result of this paper is a decomposition theorem for a measure on the one-dimensional torus. Given a sufficiently large subset $S$ of the positive integers, an arbitrary measure on the torus is decomposed as the sum of two measures. The first one $\mu_1$ has the property that the random walk with initial distribution $\mu_1$ evolved by the action of $S$ equidistributes very fast. The second measure $\mu_2$ in the decomposition is concentrated on very small neighborhoods of a small… 



The discretized sum-product and projection theorems

We give a new presentation of the discrete ring theorem for sets of real numbers [B]. Special attention is given to the relation between the various parameters. As an application, new Marstrand type

Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation

The objects of ergodic theory -measure spaces with measure-preserving transformation groups- will be called processes, those of topological dynamics-compact metric spaces with groups of homeomorphisms-will be called flows, and what may be termed the "arithmetic" of these classes of objects is concerned.

Rigidity of measures invariant under the action of a multiplicative semigroup of polynomial growth on 𝕋

Abstract We prove that if a Borel probability measure on the circle group is invariant under the action of a ‘large’ multiplicative semigroup (lower logarithmic density is positive) and the action of

Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers

LetS be a nonlacunary subsemigroup of the natural numbers and letμ be anS-invariant and ergodic measure. Using entropy arguments on a symbolic representation of the inverse limit of this action, we

Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus

Let Γ be a semigroup of d × d nonsingular integer matrices, and consider the action of Γ on the torus T. We assume throughout that the action is strongly irreducible: there is no subtorus invariant

Noncommuting random products

Introduction. Let Xy,X2, ■■-,X„,--be a sequence of independent real valued random variables with a common distribution function F(x), and consider the sums Xy + X2 + ■■• + X„. A fundamental theorem

×2 and ×3 invariant measures and entropy

Abstract Let p and q be relatively prime natural numbers. Define T0 and S0 to be multiplication by p and q (mod 1) respectively, endomorphisms of [0,1). Let μ be a borel measure invariant for both T0

Estimates for the Number of Sums and Products and for Exponential Sums in Fields of Prime Order

Our first result is a ‘sum‐product’ theorem for subsets A of the finite field Fp, p prime, providing a lower bound on max (|A + A|, |A · A|). The second and main result provides new bounds on

On a question of Erdős and Moser

For two finite sets of real numbers A and B, one says that B is sum-free with respect to A if the sum set {b + b | b, b ∈ B, b 6= b} is disjoint from A. Forty years ago, Erdős and Moser posed the

Some effective results for ×a×b

Abstract We provide effective versions of theorems of Furstenberg and Rudolph–Johnson regarding closed subsets and probability measures of ℝ/ℤ invariant under the action of a non-lacunary