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 multidimensional symbolic dynamics. I gratefully acknowledge support for my research from a Collaboration Grant for Mathematicians from the Simons Foundation.

- 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.

- Minimal zero entropy subshifts can be unrestricted along any sparse set, submitted.

- Measures of maximal entropy of bounded density subshifts (with Felipe García-Ramos and Carlos Reyes), submitted.

- Low complexity subshifts have discrete spectrum (with Darren Creutz), to appear in Forum Math. Sigma.

- 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.