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math.PR2023
Scaling limit of the occupation measure of random walk cut points
Yifan Gao, Xinyi Li, Petr Panov +1
We consider the occupation measure of the cut points of a simple random walk on a -dimensional cubic lattice for , and we show that the scaling limit of the occupation…
math.PR2018
Shape theorem and surface fluctuation for Poisson cylinders
Marcelo Hilario, Xinyi Li, Petr Panov
In this work, we prove a shape theorem for Poisson cylinders and give a power law bound on surface fluctuations. We prove that for any , conditioned on the origin b…
math.PR2018
Weighted graphs and complex Gaussian free fields
Gregory F. Lawler, Petr Panov
We prove a combinatorial lemma about the distribution of directed currents in a complex "loop soup" and use it to give a new proof of the isomorphism relating loop measures and com…