LAUSR

The local limit of uniform spanning trees

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1 Published in 2021 at "Probability Theory and Related Fields"

DOI: 10.1007/s00440-021-01072-2

Abstract: We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to $$\infty $$ ∞ is the Poisson(1) branching process conditioned to survive forever.… read more here.

Keywords: local limit; uniform spanning; spanning trees; limit uniform ... See more keywords

Exact convergence rate of the local limit theorem for branching random walks on the integer lattice

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1 Published in 2017 at "Stochastic Processes and their Applications"

DOI: 10.1016/j.spa.2016.07.015

Abstract: Consider branching random walks on the integer lattice Zd, where the branching mechanism is governed by a supercritical Galton–Watson process and the particles perform a symmetric nearest-neighbor random walk whose increments equal to zero with… read more here.

Keywords: local limit; exact convergence; random walks; convergence rate ... See more keywords

On the local times of stationary processes with conditional local limit theorems

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1 Published in 2017 at "Stochastic Processes and their Applications"

DOI: 10.1016/j.spa.2017.09.012

Abstract: We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler… read more here.

Keywords: local limit; limit theorems; conditional local; stationary processes ... See more keywords

A local limit theorem and loss of rotational symmetry of planar symmetric simple random walk

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1 Published in 2018 at "Transactions of the American Mathematical Society"

DOI: 10.1090/tran/7399

Abstract: We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points… read more here.

Keywords: local limit; simple random; limit theorem; random ... See more keywords

Error bounds in local limit theorems using Stein’s method

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1 Published in 2019 at "Bernoulli"

DOI: 10.3150/17-bej1013

Abstract: We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in the context… read more here.

Keywords: local limit; bounds local; limit theorems; stein method ... See more keywords