Ronnie Pavlov's Homepage

Contact information:

Ronnie Pavlov
Professor, Dept. of Mathematics
Office: Knudson 204
Phone: (303)-871-4001
e-mail: rpavlov at du.edu

My research interests lie primarily in ergodic theory and dynamical systems, and most of my work involves symbolic dynamics. I gratefully acknowledge support for my research from a Collaboration Grant for Mathematicians from the Simons Foundation.

Some mathematical documents
My CV (last updated in 2020) How to Give a Good Colloquium (by John McCarthy) How to Write Mathematics (by Paul Halmos)
Publications

The extended Hausdorff dimension spectrum of a conformal iterated function system is maximal (with Andrei Ghenciu), submitted.
On minimal subshifts of linear word complexity with slope less than 3/2 (with Darren Creutz), submitted.
Interpolation sets for dynamical systems (with Andreas Koutsogiannis, Anh Le, Joel Moreira, and Florian Richter), Trans. Amer. Math. Soc., to appear.
Minimal zero entropy subshifts can be unrestricted along any sparse set, Ergodic Theory Dynam. Systems, to appear.
Measures of maximal entropy of bounded density subshifts (with Felipe García-Ramos and Carlos Reyes), Ergodic Theory Dynam. Systems, to appear.
Low complexity subshifts have discrete spectrum (with Darren Creutz), Forum Math. Sigma, 11 (2023), E96.
On the structure of generic subshifts (with Scott Schmieding), Nonlinearity, 36 (2023), no. 9, 4904-4953.
Subsystem entropies of shifts of finite type and sofic shifts on countable amenable groups (with Robert Bland and Kevin McGoff), Ergodic Theory Dynam. Systems, 43 (2023), no. 9, 2881-2914.
Measure-theoretically mixing subshifts with low complexity (with Darren Creutz and Shaun Rodock), Ergodic Theory Dynam. Systems, 43 (2023), no. 7, 2293-2316.
Local finiteness and automorphism groups of low complexity subshifts (with Scott Schmieding), Ergodic Theory Dynam. Systems, 43 (2023), no. 6, 1980-2001.
Subsystems of transitive subshifts with linear complexity (with Andrew Dykstra and Nic Ormes), Ergodic Theory Dynam. Systems, 42 (2022), no. 6, 1967-1993.
On subshifts with slow forbidden word growth, Ergodic Theory Dynam. Systems, 42 (2022), no. 4, 1487-1516.
Ubiquity of entropies of intermediate factors (with Kevin McGoff), J. Lond. Math. Soc., 104 (2021), no. 2, 865-885.
The relationship between word complexity and computational complexity in subshifts (with Pascal Vanier), Discrete Contin. Dyn. Sys., 41 (2021), no. 4, 1627-1648.
On entropy and intrinsic ergodicity of coded subshifts, Proc. Amer. Math. Soc., 148 (2020), no. 11, 4717-4731.
Extender sets and measures of maximal entropy for subshifts (with Felipe García-Ramos), J. Lond. Math. Soc, 100 (2019), no. 3, 1013-1033.
On the complexity function for sequences which are not uniformly recurrent (with Nic Ormes), Contemp. Math., 736 (2019), 125-138.
One-sided almost specification and intrinsic ergodicity (with Vaughn Climenhaga), Ergodic Theory Dynam. Systems, 39 (2019), no. 9, 2456-2480.
On non-uniform specification and uniqueness of the equilibrium state in expansive systems, Nonlinearity, 32 (2019), no. 7, 2441-2466.
Factor maps and embeddings for random Z^d shifts of finite type (with Kevin McGoff), Israel J. Math., 230 (2019), no. 1, 239-273.
Follower, predecessor, and extender entropies (with Thomas French), Monatsh. Math., 188 (2019), no. 3, 495-510.
A characterization of the sets of periods within shifts of finite type (with Madeline Doering), Involve, 12 (2019), no. 2, 203-220.
Factoring onto Z^d subshifts with the finite extension property (with Raimundo Briceño and Kevin McGoff), Proc. Amer. Math. Soc. 146 (2018), no. 12, 5129-5240.
Topologically completely positive entropy and zero-dimensional topologically completely positive entropy, Ergodic Theory Dynam. Systems, 38 (2018), no. 5, 1894-1922.
Strong spatial mixing in homomorphism spaces (with Raimundo Briceño), SIAM J. Discrete Math., 31 (2017), no. 3, 2110-2137.
On factors of Z^d SFTs and intrinsic ergodicity (with Kevin McGoff), Ergodic Theory Dynam. Systems, 37 (2017), no. 2, 621-645.
Subshifts with slowly growing numbers of follower sets (with Thomas French and Nic Ormes), Contemp. Math., 678 (2016), 192-203.
Random Z^d-shifts of finite type (with Kevin McGoff), J. Mod. Dyn., 10 (2016), no. 2, 287-330.
Extender sets and multidimensional subshifts, (with Nic Ormes), Ergodic Theory Dynam. Systems, 36 (2016), no. 3, 908-923.
On intrinsic ergodicity and weakenings of the specification property, Adv. Math. 295 (2016), 250-270.
Representation and poly-time approximation for pressure of Z^2 lattice models in the non-uniqueness region (with Stefan Adams, Raimundo Briceño, and Brian Marcus), J. Stat. Phys. 162 (2016), no. 4, 1031-1067.
An integral representation for topological pressure in terms of conditional probabilities, (with Brian Marcus), Israel J. Math. 207 (2015), no. 1, 395-433.
Entropies realizable by block gluing shifts of finite type, (with Michael Schraudner), J. Anal. Math. 126 (2015), 113-174.
Classification of sofic projective subdynamics of multidimensional shifts of finite type (with Michael Schraudner), Trans. Amer. Math. Soc. 367 (2015), 3371-3421.
Entropy and measures of maximal entropy for axial powers of subshifts (with Tom Meyerovitch), Proc. Lond. Math. Soc. 109 (2014), no. 4, 921-945.
A characterization of topologically completely positive entropy for shifts of finite type, Ergodic Theory Dynam. Systems 34 (2014), no. 6, 2054-2065.
Shifts of finite type with nearly full entropy, Proc. Lond. Math. Soc. 108 (2014), no. 1, 103-132.
One dimensional Markov random fields, Markov chains and topological Markov fields (with N. Chandgotia, G. Han, B. Marcus, and T. Meyerovitch), Proc. Amer. Math. Soc. 142 (2014), no. 1, 227-242.
Computing bounds for entropy of stationary Z^d Markov random fields (with Brian Marcus), SIAM J. Discrete Math. 27 (2013), no. 3, 1544-1558.
Independence entropy of Z^d-shift spaces (with Erez Louidor and Brian Marcus), Acta. Appl. Math. 126 (2013), 297-317.
Approximating entropy for a class of Z^2 Markov random fields and pressure for a class of functions on Z^2 shifts of finite type (with Brian Marcus), Ergodic Theory Dynam. Systems 33 (2013), no. 1, 186-220.
A class of nonsofic multidimensional shift spaces, Proc. Amer. Math. Soc. 141 (2013), no. 3, 987-996.
Approximating the hard square entropy constant with probabilistic methods, Ann. Probab. 40 (2012), no. 6, 2362-2399.
Perturbations of multidimensional shifts of finite type, Ergodic Theory Dynam. Systems 31 (2011), no. 2, 483-526.
Multidimensional sofic shifts without separation and their factors (with Mike Boyle and Michael Schraudner), Trans. Amer. Math. Soc. 362 (2010), 4617-4653.
Some counterexamples in topological dynamics, Ergodic Theory Dynam. Systems 28 (2008), no. 4, 1291-1322.