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Subsystems Of Transitive Subshifts With Linear Complexity, Andrew Dykstra, Nicholas Ormes, Ronnie Pavlov
Subsystems Of Transitive Subshifts With Linear Complexity, Andrew Dykstra, Nicholas Ormes, Ronnie Pavlov
Mathematics: Faculty Scholarship
We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [On the complexity function for sequences which are not uniformly recurrent. Dynamical Systems and Random Processes (Contemporary Mathematics, 736). American Mathematical Society, Providence, RI, 2019, pp. 125--137]. We also bound the number of generic measures such a subshift can support based on its complexity function. Our measure-theoretic bounds generalize those of Boshernitzan [A unique ergodicity of minimal symbolic flows with linear block growth. J. Anal. Math.44(1) (1984), 77–96] and are closely related to those of Cyr and Kra …
On Subshifts With Slow Forbidden Word Growth, Ronnie Pavlov
On Subshifts With Slow Forbidden Word Growth, Ronnie Pavlov
Mathematics: Faculty Scholarship
In this work, we treat subshifts, defined in terms of an alphabet A and (usually infinite) forbidden list F, where the number of n-letter words in F has ‘slow growth rate’ in n. We show that such subshifts are well behaved in several ways; for instance, they are boundedly supermultiplicative in the sense of Baker and Ghenciu [Dynamical properties of S-gap shifts and other shift spaces. J. Math. Anal. Appl.430(2) (2015), 633–647] and they have unique measures of maximal entropy with the K-property and which satisfy Gibbs bounds on large (measure-theoretically) sets. The main tool in our proofs is a …
Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill
Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill
Electronic Theses and Dissertations
Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra VG is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by VG if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, VG will also be strongly finitely generated. This is an analogue …
Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse
Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse
Electronic Theses and Dissertations
Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …