November 15, 2025Random Structures and Algorithms

Scaling Limit of Critical Percolation Clusters on Hyperbolic Random Half‐Planar Triangulations and the Associated Random Walks

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Authors

EAEleanor Archer DCDavid A. Croydon

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Implication

This analysis shows the scaling limit of critical percolation clusters and random walks in hyperbolic geometries, indicating the emergence of Brownian motion.

Key Points

Brownian motion emerges as the scaling limit of random walks on critical percolation clusters in hyperbolic geometric structures.
Key findings include the scaling limit of percolation clusters aligning with the properties of Brownian motion within geometric contexts.
The analysis uses methods involving scaling limits and Gromov-Hausdorff-Prohorov approaches to assess percolation phenomena.
Findings suggest the importance of scaling limits in studying random walks on complex geometric frameworks.

Cite This Study

Archer et al. (2025) studied this question.

synapsesocial.com/papers/69251994c0ce034ddc353692 https://doi.org/10.1002/rsa.70020

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Implication

This analysis shows the scaling limit of critical percolation clusters and random walks in hyperbolic geometries, indicating the emergence of Brownian motion.

Scaling Limit of Critical Percolation Clusters on Hyperbolic Random Half‐Planar Triangulations and the Associated Random Walks

Discussion

Member takes

Implication

Key Points

Cite This Study

Scaling Limit of Critical Percolation Clusters on Hyperbolic Random Half‐Planar Triangulations and the Associated Random Walks

Discussion

Member takes

Implication

Key Points

Cite This Study

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