Work

Spanning k-Trees and Loop-Erased Random Surfaces

Year: 2017

Type: article

Abstract: We introduce a novel model of random hypersurfaces that generalizes loop-erased random walk.Using a duality with loop-erased random walk we show that if these surfaces have a growth exponent α then 2 < α ≤ 8 / 3 in three dimensions.We further present numerical evidence from experiment that the growth exponent is 2.5269 ± 0.0017 in 3 dimensions.The behavior is very dierent in d ≥ 4 dimensions where we show that this growth exponent exists and is d.We also study the dimension 1 homology of 2-dimensional random acyclic complexes chosen approximately uniformly.We present numerical evidence that this model of a random group is distributed according to the CohenLenstra heuristics.

Source: OhioLink ETD Center (Ohio Library and Information Network)

Author: Kyle Parsons

Institution: The Ohio State University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2799458799

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