quantitative recurrence
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2018 ◽  
Vol 147 (4) ◽  
pp. 1453-1465
Author(s):  
Yuanyang Chang ◽  
Min Wu ◽  
Wen Wu


2018 ◽  
Vol 18 (03) ◽  
pp. 1850003
Author(s):  
Nuno Luzia

First, we prove an almost sure local central limit theorem for lattice random walks in the plane. The corresponding version for random walks in the line has been considered previously by the author. This gives us an extension of Pólya’s Recurrence Theorem, namely we consider an appropriate subsequence of the random walk and give the asymptotic number of returns to the origin and other states. Secondly, we prove an almost sure local central limit theorem for (not necessarily lattice) random walks in the line or in the plane, which will also give us quantitative recurrence results. Finally, we prove a version of the almost sure central limit theorem for multidimensional random walks. This is done by exploiting a technique developed by the author.



Nonlinearity ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 864-886 ◽  
Author(s):  
Maria Carvalho ◽  
Fagner B Rodrigues ◽  
Paulo Varandas


2018 ◽  
Vol 170 (5) ◽  
pp. 862-882 ◽  
Author(s):  
Stefano Galatolo ◽  
Isaia Nisoli ◽  
Maria Jose Pacifico


2018 ◽  
Vol 22 (1) ◽  
pp. 225-244 ◽  
Author(s):  
Cao Zhao ◽  
Ercai Chen


2017 ◽  
Vol 145 (11) ◽  
pp. 4751-4761 ◽  
Author(s):  
André Junqueira


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