Internal DLA generated by cookie random walks on $\mathbb{Z}$
Olivier Raimond (MODAL'X), Bruno Schapira (LM-Orsay)
TL;DR
This paper establishes a law of large numbers for the boundary growth in a one-dimensional internal DLA model driven by cookie random walks, using stochastic algorithms techniques.
Contribution
It introduces a law of large numbers for internal DLA boundaries generated by cookie random walks in one dimension, a novel result in this context.
Findings
Law of large numbers for the right boundary in 1D internal DLA
Application of stochastic algorithms techniques to boundary analysis
New insights into cookie random walk-driven growth processes
Abstract
We prove a law of large numbers for the right boundary in the model of internal DLA generated by cookie random walks in dimension one. The proof is based on stochastic algorithms techniques.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Theoretical and Computational Physics