Renormalization Group Solution of the Chutes&Ladder Model Pubblico

Abstract

We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps we find with exact renormalization group calculations that there is a dynamical transition between a localized adsorption phase and an anomalous diffusion phase in which the mean-square displacement exponent depends non-universally on the bias of the system. We compare these results with similar findings of unconventional phase behavior in hierarchical networks, as well as with related systems involving Levy-distributed backjumps.

Table of Contents

Table of Contents

1. Introduction

1.1 Introduction to scaling behavior and universality

1.2 Background of Rrenormalization Group

1.3 Motivation

2. Network Design

3. Renormalization Group Analysis

4. Conclusion

5. References

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	BS
Submission	Honors Thesis
Language	English
Research Field	Physics, General Physics, Theory
Parola chiave	Random Walk Universality Hierarchical network Anomalous diffusion Renormalization group
Committee Chair / Thesis Advisor	Boettcher, Stefan, Emory University
Committee Members	Dale III, Horace, Emory University Raman, Parimala, Emory University

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