## Research papers and surveys
Title-links are to the Mathematics arXiv. Writings marked `Preprint' may not be in their final form.
### Research
Classical analysis
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
### Surveys
*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
*
* |