The wreath product of Z with Z has Hilbert compression exponent 2 3 (2009)
Tim Austin, Assaf Naor, Yuval Peres
Let G be a finitely generated group, equipped with the word metric d associated with some finite set of generators. The Hilbert compression exponent of G is the supremum over all α ≥ 0 such that...
Pleasant extensions retaining algebraic structure, II (2009)
This paper is the second of three in which we develop and use some general machinery for constructing extensions of probability-preserving systems in which certain nonconventional ergodic averages...
Pleasant extensions retaining algebraic structure, III (2009)
This is the last of three papers (following arXiv:0905.0518 and arXiv:0910.0907) in which we develop and use some general machinery for extending probability-preserving \bbZ^d-systems so as to obtain...
A counterexample to a conjecture of Atiyah (2009)
We prove that there are examples of finitely generated groups G together with group ring elements Q \in \bbQ G for which the von Neumann dimension \dim_{LG}\ker Q is irrational, so (in conjunction...
A finitely-generated amenable group with very poor compression into Lebesgue spaces (2009)
We construct an example of a finitely-generated amenable group that does not admit any coarse 1-Lipschitz embedding with positive compression exponent into L_p for any 1 \leq p < \infty, answering...
Relatively finite measure-preserving extensions and lifting multipliers by Rokhlin cocycles (2009)
Austin, Tim, Lemanczyk, Mariusz
We show that under some natural ergodicity assumptions extensions given by Rokhlin cocycles lift the multiplier property if the associated locally compact group extension has only countably many...
A CAT(0)-valued pointwise ergodic theorem (2009)
In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued...
We study a generalized notion of a homogeneous skew-product extension of a probability-preserving base system in which the homogeneous space fibres can vary over the ergodic decomposition of the...
Pleasant extensions retaining algebraic structure, I (2009)
In two recent papers we introduced some new techniques for extending a probability-preserving system T:\bbZ^d\actson (X,\mu) to an enlarged system enjoying certain desirable properties for the...
Deducing the Density Hales-Jewett Theorem from an infinitary removal lemma (2009)
We offer a new proof of Furstenberg and Katznelson's density version of the Hales-Jewett Theorem: For any $\delta > 0$ there is some $N_0 \geq 1$ such that whenever $A \subseteq [k]^N$ with $N \geq...
Deducing the multidimensional Szemeredi Theorem from an infinitary removal lemma (2008)
We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving transformations T_1, T_2, >..., T_d: \bbZ\curvearrowright (X,\S,\mu), and...
On the geometry of a class of invariant measures and a problem of Aldous (2008)
In his 1985 survey of notions of exchangeability, Aldous introduced a form of exchangeability corresponding to the symmetries of the infinite discrete cube, and asked whether these exchangeable...
On the norm convergence of nonconventional ergodic averages (2008)
We offer a generalization of the recent result of Tao (building on earlier results of Conze and Lesigne, Furstenberg and Weiss, Zhang, Host and Kra, Frantzikinakis and Kra and Ziegler) that the...
On the testability and repair of hereditary hypergraph properties (2008)
Recent works of Alon-Shapira and R\"odl-Schacht have demonstrated that every hereditary property of undirected graphs or hypergraphs is testable with one-sided error; informally, this means that if a...
On exchangeable random variables and the statistics of large graphs and hypergraphs (2008)
De Finetti's classical result of [18] identifying the law of an exchangeable family of random variables as a mixture of i.i.d. laws was extended to structure theorems for more complex notions of...
The wreath product of Z with Z has Hilbert compression exponent 2/3 (2007)
Austin, Tim, Naor, Assaf, Peres, Yuval
Let G be a finitely generated group, equipped with the word metric d associated with some finite set of generators. The Hilbert compression exponent of G is the supremum over all $\alpha\ge 0$ such...
The Euclidean distortion of the lamplighter group (2007)
Austin, Tim, Naor, Assaf, Valette, Alain
We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion ${\rm O}(\sqrt{\log n})$. This matches the lower bound proved by Lee, Naor and Peres in...
The Euclidean distortion of the lamplighter group (2007)
Tim Austin, Assaf Naor, Alain Valette
We show that the cyclic lamplighter group C2 ≀ Cn embeds into Hilbert space with distortion O ( √ log n). This matches the lower bound proved by Lee, Naor and Peres in [14], answering a question...
What should we look for in kid's multimedia? (2002)
Typescript (photocopy) "Masters by Project"--Cover. Cover title.