Tim Austin

activity

20062021

most citedOn exchangeable random variables and the statistics of large graphs and hypergraphs

72 citations · 401 across the 40 of their papers we have counts for

collaborators

Showing math.PRShow all

9 papers · 1 filter

math.PR2018

The structure of low-complexity Gibbs measures on product spaces

Tim Austin

Let $K_{1}$ , $\dots$ , $K_{n}$ be bounded, complete, separable metric spaces. Let $λ_{i}$ be a Borel probability measure on $K_{i}$ for each $i$ . Let $f : \prod_{i} K_{i} \to R$ be a bou…

math.PR2018★ 2 cited

Multi-variate correlation and mixtures of product measures

Tim Austin

Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$ -tuple of random variables. They both reduce to mutual in…

math.PR2017★ 8 cited

Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees

Tim Austin, Moumanti Podder

Consider a statistical physical model on the $d$ -regular infinite tree $T_{d}$ described by a set of interactions $Φ$ . Let ${G_{n}}$ be a sequence of finite graphs with vertex se…

math.PR2013★ 9 cited

Exchangeable random measures

Tim Austin

Let A be a standard Borel space, and consider the space A^{\bbN^{(k)}} of A-valued arrays indexed by all size-k subsets of \bbN. This paper concerns random measures on such a space…

math.PR2013★ 5 cited

A hierarchical version of the de Finetti and Aldous-Hoover representations

Tim Austin, Dmitry Panchenko

We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree struct…

math.PR2009

Deducing the Density Hales-Jewett Theorem from an infinitary removal lemma

Tim Austin

We offer a new proof of Furstenberg and Katznelson's density version of the Hales-Jewett Theorem: For any $δ > 0$ there is some $N_{0} \geq 1$ such that whenever $A \subseteq [k]^{N}$ w…