Explore the Frontier of Global Academia

AcademicHub aggregates real-time literature from top journals and preprint platforms. Build your personal research radar and let large language models compile cross-disciplinary analysis briefings automatically.

Authors: Robin Kaiser ×

↻ Shuffle

01.

arXiv (math.PR) 2026-06-11 DOI: arXiv:2603.12006

On the structure of the sandpile identity element on Sierpinski gasket graphs

Authors:

Robin Kaiser ↗Ecaterina Sava-Huss ↗Julia \"Uberbacher ↗

arXiv:2603.12006v2 Announce Type: replace-cross Abstract: We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpinski gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs.

Read & Discuss → View Source →

02.

arXiv (math.PR) 2026-06-18 DOI: arXiv:2606.19131

Law of the Iterated Logarithm for $p$-Walks on $\mathbb{Z}$

Authors:

Robin Kaiser ↗

arXiv:2606.19131v1 Announce Type: new Abstract: The $p$-rotor walk on $\mathbb{Z}$ is a self-interacting walk that interpolates between the simple random walk and the deterministic rotor walk. While the weak convergence of this model to a perturbed Brownian motion is known, its almost sure asymptotic boundaries have not been characterized. In this paper, we establish the exact Law of the Iterated Logarithm (LIL) for the $p$-rotor walk. Utilizing the decomposition of the walk into a martingale perturbed by its running extrema, we obtain first a functional Law of the Iterated Logarithm for the linearly interpolated paths of the $p$-walk. We then obtain the classical LIL constants by solving a calculus of variations problem over the perturbed Strassen set.

Read & Discuss → View Source →