Kolmogorov complexity and the geometry of Brownian motion
Willem L. Fouche
TL;DR
This paper explores the geometric properties of Brownian motion through the lens of Kolmogorov-Chaitin complexity, revealing how algorithmic randomness influences the formation of complex geometric patterns.
Contribution
It extends the understanding of Brownian motion by integrating Kolmogorov complexity, providing new insights into the randomness and geometry of Brownian paths.
Findings
Kolmogorov-Chaitin complexity characterizes Brownian motion geometry
Random geometric patterns are linked to algorithmic randomness
Enhanced understanding of Brownian motion structure
Abstract
In this paper, we continue the study of the geometry of Brownian motions which are encoded by Kolmogorov-Chaitin random reals (complex oscillations). We unfold Kolmogorov-Chaitin complexity in the context of Brownian motion and specifically to phenomena emerging from the random geometric patterns generated by a Brownian motion.
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