Anthony Quas's Papers

• Universal gap growth for Lyapunov exponents of perturbed matrix products (with J. Atnip, G. Froyland, C. González-Tokman) (submitted).
• Asymptotic behavior of the pressure function for Hölder potentials (with T. Kucherenko) (submitted).
• Realization of Anosov diffeomorpshisms on the torus (with T. Kucherenko), J. London Math. Soc. (to appear).
• Generation of measures by statistics of rotations along sets of integers (with E. Lesigne, J. Rosenblatt and M. Wierdl) Indiana U. Math. J. (to appear).
• Lyapunov exponents of orthogonal-plus-normal cocycles (with S. Bednarski) Nonlinearity 38 (2025), 035007.
• A multiplicative ergodic theoretic characterization of relative equilibrium states (with J. Antonioli and S. Hong) Ergodic Theory Dynam. Syst. 43 (2023), 1455-1470.
• The lightning model (with J. Campbell and A. Deane) J. Theor. Prob. 35 (2022), 2738-2756.
• Flexibility of the Pressure function (with T. Kucherenko) Commun. Math. Phys. 395 (2022), 1431-1461.
• Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach (with C. González-Tokman), Tr. Mosk. Math. Obs. (Transactions of the Moscow Mathematical Society) 82 (2021), 65-76 [invited paper in honour of 80th birthday of Valery Oseledets].
• Random Composition of L-S-V Maps Sampled Over Large Parameter Ranges (with C. Bose and M. Tanzi) Nonlinearity 34 (2021), 3641-3675.
• Stability and Collapse of the Lyapunov spectrum for Perron-Frobenius Operator cocycles (with C. González-Tokman) J. Eur. Math. Soc. 23 (2021), 3419-3457.
• Multiple phase transitions on compact symbolic systems (with T. Kucherenko and C. Wolf), Adv. Math. 385 (2021), 107768.
• Geometric random graphs and Rado sets of continuous functions (with A. Bonato and J. Janssen), Discrete Analysis 2021:3.
• Support stability of maximizing measures for shifts of finite type (with J.S. Gonschorowski and J. Siefken) Ergodic Theory Dynam. Syst. 41 (2021), 869-880.
• Explicit bounds for separation between Oseledets subspaces (with P. Thieullen and M. Zarrabi) Dynam. Syst. 34 (2019), 517--560.
• Hilbert Space Lyapunov Exponent stability (with G. Froyland and C. González-Tokman) Trans. Amer. Math. Soc. 372 (2019), 2357--2388.
• Geometric random graphs and Rado sets in sequence spaces (with A. Bonato and J. Janssen) Eur. J. Comb. 79 (2019), 1-14.
• On irreducibility of Oseledets subspaces (with C. Bose and J. Horan) Dynamical Systems: An International Journal 33 (2018), 332--347.
• The variation of invariant graphs in forced systems (with B. Fernandez), Chaos 083101 (2018).
• Dynamical analysis of a repeated game with incomplete information (with X. Bressaud) Math. of Oper. Res. 42 (2017), 1085--1105.
• Bratteli diagrams where random orders are imperfect (with J. Janssen and R. Yassawi) Proc. Amer. Math. Soc. 145 (2017), 721-735.
• Computing automorphism groups of shifts using atypical equivalence classes (with E. Coven and R. Yassawi) Discrete Analysis 2016:3.
• A monotone Sinai theorem (with T. Soo) Ann. Prob. 44 (2016), 107-130.
• Ergodic universality of some topological dynamical systems (with T. Soo) Trans. Amer. Math. Soc. 368 (2016), 4137-4170.
• Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles (with G. Froyland and C. González-Tokman) Comm. Pure Appl. Math. 68 (2015), 2052-2081.
• A concise proof of the Multiplicative Ergodic Theorem on Banach Spaces (with C. González-Tokman) J. Mod. Dyn. 9 (2015), 237-255.
• Rudolph's two step coding theorem and Alpern's lemma for R^d actions (with B. Kra and A. Şahin) Trans. Amer. Math. Soc. 367 (2015), 4253-4285.
• Detecting Isolated Spectrum of Transfer and Koopman Operators with Fourier Analytic Tools (with G. Froyland and C. González-Tokman) J. Comput. Dyn. 1 (2014), 249-278.
• Stability and approximation of random invariant densities for Lasota-Yorke map cocycles (with G. Froyland and C. González-Tokman) Nonlinearity 27 (2014), 647-660.
• A semi-invertible operator Oseledets theorem (with C. González-Tokman), Ergodic Theory and Dynamical Systems 34 (2014), 1230-1272.
• A semi-invertible Oseledets theorem with applications to transfer operator cocycles (with G. Froyland and S. Lloyd) Discrete and Continuous Dynamical Systems 33 (2013), 3835-3860.
• Class degree and relative maximal entropy (with M. Allahbakhshi) Trans. Amer. Math. Soc. 365 (2013), 1347-1368.
• Weak mixing suspension flows over shifts of finite type are universal (with T. Soo), Journal of Modern Dynamics 6 (2012), 427-449.
• Piecewise isometries, uniform distribution and 3 log(2)-π²/8 (with Y. Cheung and A. Goetz) Ergodic Theory Dynamical Systems 32 (2012), 1862-1888.
• Ergodic optimization of super-continuous functions (with J. Siefken) Ergodic Theory Dynamical Systems 32 (2012), 2071-2082.
• Statistical properties of invariant graphs in piecewise affine discontinuous forced systems (with B. Fernandez) Nonlinearity 24 (2011), 2477-2488.
• Entropy Rate for Hidden Markov Chains with Rare Transitions (with Y. Peres) in Entropy of Hidden Markov Chains and Connections to Dynamical Systems, London Mathematical Society Lecture Notes in Mathematics, Cambridge 2011.
• Coherent structures and isolated spectrum for Perron-Frobenius cocycles (with G. Froyland and S. Lloyd) Ergodic Theory and Dynamical Systems 30 (2010), 729-756.
• Rates of divergence of non-conventional ergodic averages (with M. Wierdl) Ergodic Theory and Dynamical Systems 30 (2010), 233--262.
• Ergodicity and Mixing. Chapter in Encyclopedia of Complex Systems, Springer 2009.
• Distances in Positive Density Sets J. Comb. Th. A 116 (2009) 979-987.
• Global Properties of Piecewise Isometries (with A. Goetz) Ergodic Theory and Dynamical Systems 29 (2009), 545-568.
• Generalized polynomials and mild mixing systems (with R. McCutcheon) Canadian J. Math. 61 (2009) 656-673.
• Deterministic representation for position dependent random maps. (with W. Bahsoun and C. Bose) Discrete Contin. Dynam. Systems 22 (2008) 529--540.
• Balanced Sets and the Vector Game (with Z. Nedev) International J. Number Th. 4 (2008) 339-347.
• Rates of approximation of minimizing measures (with X. Bressaud) Nonlinearity 20 (2007), 845-853.
• Ergodic averages along the squares (with M. Wierdl) Appendix to 'Combinatorial and Diophantine Applications of Ergodic Theory' by V. Bergelson, in Handbook of Dynamical Systems (Volume 1B)(2006), 853--864.
• Approximate transitivity for zero entropy systems (with A. Dooley) Ergodic Theory Dynamical Systems 25 (2005), 443--453.
• Ergodic averaging sequences; (with M. Boshernitzan, G. Kolesnik and M. Wierdl) J. d'Anal. Math 95 (2005) 63--103.
• Percolation in Voronoi tilings; (with P. Balister and B. Bollobás) Random Struct. Alg. 26 (2005) 310-318.
• Anomalous outcomes in preferential votingStochastics and Dynamics 4 (2004), 95--105.
• Weak-L¹ estimates and ergodic theorems (with C. Demeter) New York J. Math. 10 (2004), 169--174.
• Periodicity and local complexity (with L. Zamboni) Theor. Comp. Sci. 319 (2004), 229--240.
• Generic points in Cartesian powers of the Morse dynamical system (with E. Lesigne and M. Wierdl) ;Bull. Soc. Math. France 131 (2003), 435--464.
• Entropy gaps and locally maximal entropy in Z^d subshifts (with A. Şahin) Ergodic Theory Dynamical Systems 23 (2003), 1227--1245.
• Measures of relatively maximal entropy; (with K. Petersen and S. Shin) Ergodic Theory Dynam. Systems 23 (2003) 207--223.
• Entropy along convex shapes, random tilings and shifts of finite type; (with P. Balister and B. Bollobás) Illinois J. Math 46 (2002) 781--795.
• Mappings of group shifts; (with P. Trow) Israel J. Math 124 (2001) 333--365.
• A generic C¹ expanding map has a singular S-R-B measure (with J. Campbell) Comm. Math. Phys. 221 (2001) 335--349.
• Subshifts of multi-dimensional shifts of finite type; (with P. Trow) Ergodic Theory Dynam. Systems 20 (2000) 859--874.
• Infinite paths in a Lorentz lattice gas model;Probab. Theory Related Fields 114 (1999) 229--244.
• Scaling Functions And Gibbs Measures And Teichmüller Spaces Of Circle Endomorphisms; (with G. Cui and Y. Jiang) Discrete Contin. Dynam. Systems 5 (1999) 535--552.
• An entropy estimator for a class of infinite alphabet processes Teor. Veroyatnost. i Primenen 43 (1999) 496--507.
• Most expanding maps have no absolutely continuous invariant measure Studia Math. 134 (1999) 69--78.
• Product and Markov measures of type III; (with A. Dooley and I. Klemes) J. Austral. Math. Soc. Ser. A 65 (1998) 84--110.
• Criteria for d-bar continuity; (with Z. Coelho) Trans. Amer. Math. Soc. 350 (1998) 3257--3268.
• Rigidity of continuous coboundaries;Bull. London Math. Soc. 29 (1997) 595--600.
• Invariant densities for C¹ maps;Studia Math. 120 (1996) 83--88.
• A C¹ expanding map of the circle which is not weak-mixing;Israel J. Math. 93 (1996) 359--372.
• Non-ergodicity for C¹ expanding maps and g-measures;Ergodic Theory Dynamical Systems 16 (1996) 531--543.
• Representation of Markov Chains on tori; Random Comput. Dynam. 1 (1992/3) 261--276.
• Invariant measures for families of circle maps; Math. Proc. Cambridge Philos. Soc. 111 (1992), 585--597.
• On representations of Markov chains by random smooth maps Bull. London Math. Soc. 23 (1991), 487--492.