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20052026
most citedZipf Law for Brazilian Cities

76 citations

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math.PR2025

Nonparametric estimation of the jump rate in mean field interacting systems of neurons

Aline Duarte, Kadmo Laxa, Eva Löcherbach +1

We consider finite systems of interacting neurons described by non-linear Hawkes processes in a mean field frame. Neurons are described by their membrane potential. They spike…

math.PR2017★ 55 cited

A strong invariance principle for the elephant random walk

Cristian F. Coletti, Renato Gava, Gunter M. Schütz

We consider a non-Markovian discrete-time random walk on with unbounded memory called the elephant random walk (ERW). We prove a strong invariance principle for the ER…

math.PR2014

Characterization of the stability of chains associated with -measures

Christophe Gallesco, Sandro Gallo, Daniel Yasumasa Takahashi

In this paper we introduce a notion of asymptotic stability of a probability kernel, which we call dynamic uniqueness. We say that a kernel exhibits dynamic uniqueness if all the s…

math.PR2014

Dynamical systems with heavy-tailed random parameters

Vladimir Belitsky, Mikhail Menshikov, Dimitri Petritis +1

Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for t…

math.PR2008★ 37 cited

Sharp error terms for return time statistics under mixing conditions

Miguel Abadi, Nicolas Vergne

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S…