Research papers and surveys

Title-links are to the Mathematics arXiv. Writings marked `Preprint' may not be in their final form.

Research

Classical analysis

• "On contractive families and a fixed-point question of Stein", Mathematika 52 (2005), no. 1-2, 115--129
• "A pair of non-homeomorphic product measures on the Cantor set", Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 103--110

Exchangeable random variables and related extremal combinatorics

• "On the testability and repair of hereditary hypergraph properties", with Terence Tao, Random Struct. Alg. 36 (2010), no. 4, 373--463
• "Exchangeable random measures", Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015), no. 3, 842--861
• "A hierarchical version of the de Finetti and Aldous-Hoover representations", with Dmitry Panchenko, Probab. Theory Related Fields 159 (2014), no. 3--4, Page 809--823.

High-dimensional probability and information theory

• "On the failure of concentration for the \ell_\infty ball", Israel J. Math. 211 (2016), no. 1, 221--238.
• "Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees", with Moumanti Podder, J. Stat. Phys. 170 (5), 932--951.
• "Multi-variate correlation and mixtures of product measures", Kybernetika 56 (2020), no. 3, 459--499. (Also: free online access at the journal website.)
• "The structure of low-complexity Gibbs measures on product spaces", Ann. Probab. 47 (2019), no. 6, 4002--4023.

Ergodic theory: entropy and classification

• "Scenery entropy as an invariant of RWRS processes", preprint.
• "Entropy of probability kernels from the backwards tail boundary", Studia Math. 227 (2015), no. 3, 249--257.
• "Additivity properties of sofic entropy and measures on model spaces", Forum Math. Sigma 4 (2016), e25, 79 pp.
• "The geometry of model spaces for probability-preserving actions of sofic groups", Anal. Geom. Metr. Spaces 4 (2016), Art. 6.
• "Uniform mixing and completely positive sofic entropy", with Peter Burton, J. Anal. Math. 138 (2019), no. 2, 597--612.
• "Behaviour of entropy under bounded and integrable orbit equivalence", Geom. Funct. Anal. 26 (2016), 1483--1525.
• "An asymptotic equipartition property for measures on model spaces", Trans. Amer. Math. Soc. 371 (2019), 1379--1402.
• "Measure concentration and the weak Pinsker property", Publ. Math. Inst. Hautes Études Sci. 128 (2018), 1--119.
• "A new dynamical proof of the Shmerkin--Wu theorem", J. Modern Dynam. 18 (2022), 1--11.
• "An ergodic system is dominant exactly when it has positive entropy", with Eli Glasner, Jean-Paul Thouvenot, and Benjamin Weiss. To appear, Ergodic Theory and Dynam. Systems.

Ergodic theory: multiple recurrence and related arithmetic combinatorics

• "On the norm convergence of nonconventional ergodic averages", Ergodic Theory and Dynamical Systems 30 (2010), no. 2, 321--338
• "Deducing the multidimensional Szemeredi Theorem from an infinitary removal lemma", J. Anal. Math. 111 (2010), 131--150
• "Deducing the Density Hales-Jewett Theorem from an infinitary removal lemma", J. Theoret. Probab. 24 (2011), no. 3, 615--633
• "Relatively finite measure-preserving extensions and lifting multipliers by Rokhlin cocycles", with Mariusz Lemanczyk, J. Fixed Point Theory Appl. 6 (2009), no. 1, 115--131
• "Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applications", Fund. Math. 210 (2010), no. 2, 133--206
• "Pleasant extensions retaining algebraic structure, I", J. Anal. Math. 125 (2015), 1--36
• "Pleasant extensions retaining algebraic structure, II", J. Anal. Math. 126 (2015), 1--111
• "An alternative ending to ``Pleasant extensions retaining algebraic structure'' ". Unpublished note (2010).
• "Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems", with Tanja Eisner and Terence Tao, Pacific J. Math. 250 (2011), no. 1, 1--60
• "Norm convergence of continuous-time polynomial multiple ergodic averages", Ergodic Theory Dynam. Systems 32 (2012), no. 2, 361--382. Dedicated to the memory of Dan Rudolph.
• "Ergodic-theoretic implementations of the Roth density-increment argument", Online J. Anal. Comb. (2013), no. 8, 33pp
• "Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups", Ergodic Theory Dynam. Systems 33 (2013), no. 6, 1667--1708
• "Non-conventional ergodic averages for several commuting actions of an amenable group", J. Anal. Math. 130 (2016), 243--274
• "A proof of Walsh's convergence theorem using couplings". Int. Math. Res. Not. IMRN 2015, no. 15, 6661--6674
• "Quantitative equidistribution for certain quadruples in quasi-random groups", Combin. Probab. Comput. 24 (2015), no. 2, 376--381
• "Ajtai-Szemeredi Theorems over quasirandom groups", Recent trends in combinatorics, 453–484, IMA Vol. Math. Appl., 159, Springer, [Cham], 2016

Geometry of groups and related dynamics

• "The Euclidean distortion of the lamplighter group", with Assaf Naor and Alain Valette, Discrete and Computational Geometry 44 (2010), no. 1, 55--74
• "The wreath product of Z with Z has Hilbert compression exponent 2/3", with Assaf Naor and Yuval Peres, Proc. Amer. Math. Soc. 137 (2009), no. 1, 85--90
• "A CAT(0)-valued pointwise ergodic theorem", J. Topology and Analysis 3 (2011), no. 2, 145--152.
• "Amenable groups with very poor compression into Lebesgue spaces", Duke Mathematical Journal 159 (2011), no. 2, 187--222.
• "Rational group ring elements with kernels having irrational dimension", Proc. London Math. Soc. 107 (2013), 1424--1448.
• "Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces", with Assaf Naor and Romain Tessera, Groups Geom. Dyn. 7 (2013), no. 3, 497--522.
• "Integrable measure equivalence for groups of polynomial growth", with Appendix B by Lewis Bowen, Groups Geom. Dyn. 10 (2016), no. 1, 117--154.

Cohomology of groups, topological algebra

• "Continuity properties of measurable group cohomology", with Calvin C. Moore, Math. Ann. 356 (2013), no. 3, 885--937.
• "On discontinuities of cocycles in cohomology theories for topological groups", unpublished manuscript.
• "Partial difference equations over compact Abelian groups, I: modules of solutions", preprint.
• "Partial difference equations over compact Abelian groups, II: step-polynomial solutions", preprint.
• "Euclidean-valued group cohomology is always reduced", J. Topology and Analysis 10 (2018), no. 3, 483--491.

Applied probability and stochastic processes

• "The emergence of the deterministic Hodgkin-Huxley equations as a limit from the underlying stochastic ion-channel mechanism", Ann. App. Probab. 18 (2008), no. 4, 1279--1325
• "For what number of cars must self organization occur in the Biham-Middleton-Levine traffic model from any possible starting configuration?". Unpublished note (2006), with Itai Benjamini

Surveys

• "On exchangeable random variables and the statistics of large graphs and hypergraphs", Probability Surveys 5 (2008), 80--145
• "Multiple recurrence and the structure of probability-preserving systems" (2010). This is a slightly re-written version of my thesis.

Tim Austin,
Math Sciences Building, office 6232
UCLA Mathematics Department, Box 951555, Los Angeles CA 90095-1555, U.S.A.
timaustin AT g DOT ucla DOT edu