### Abstract

We prove functional laws of the iterated logarithm for L^{0}_{n}, the number of returns to the origin, up to step n, of recurrent random walks on Z^{2} with slowly varying partial Green's function. We find two distinct functional laws of the iterated logarithm depending on the scaling used. In the special case of finite variance random walks, we obtain one limit set for L^{0}n^{cursive Greek chi}/(log n log_{3} n) ; 0 ≤ cursive Greek chi ≤ 1, and a different limit set for L^{0}_{cursive Greek chin}/(log n log_{3} n) ; 0 ≤ cursive Greek chi ≤ 1. In both cases the limit sets are classes of distribution functions, with convergence in the weak topology.

Original language | English |
---|---|

Pages (from-to) | 545-563 |

Number of pages | 19 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 34 |

Issue number | 4 |

Publication status | Published - Jul 1998 |

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### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

^{2}.

*Annales de l'institut Henri Poincare (B) Probability and Statistics*,

*34*(4), 545-563.

**Functional laws of the iterated logarithm for local times of recurrent random walks on Z ^{2}.** / Csáki, Endre; Révész, Pál; Rosen, Jay.

Research output: Contribution to journal › Article

^{2}',

*Annales de l'institut Henri Poincare (B) Probability and Statistics*, vol. 34, no. 4, pp. 545-563.

^{2}. Annales de l'institut Henri Poincare (B) Probability and Statistics. 1998 Jul;34(4):545-563.

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TY - JOUR

T1 - Functional laws of the iterated logarithm for local times of recurrent random walks on Z2

AU - Csáki, Endre

AU - Révész, Pál

AU - Rosen, Jay

PY - 1998/7

Y1 - 1998/7

N2 - We prove functional laws of the iterated logarithm for L0n, the number of returns to the origin, up to step n, of recurrent random walks on Z2 with slowly varying partial Green's function. We find two distinct functional laws of the iterated logarithm depending on the scaling used. In the special case of finite variance random walks, we obtain one limit set for L0ncursive Greek chi/(log n log3 n) ; 0 ≤ cursive Greek chi ≤ 1, and a different limit set for L0cursive Greek chin/(log n log3 n) ; 0 ≤ cursive Greek chi ≤ 1. In both cases the limit sets are classes of distribution functions, with convergence in the weak topology.

AB - We prove functional laws of the iterated logarithm for L0n, the number of returns to the origin, up to step n, of recurrent random walks on Z2 with slowly varying partial Green's function. We find two distinct functional laws of the iterated logarithm depending on the scaling used. In the special case of finite variance random walks, we obtain one limit set for L0ncursive Greek chi/(log n log3 n) ; 0 ≤ cursive Greek chi ≤ 1, and a different limit set for L0cursive Greek chin/(log n log3 n) ; 0 ≤ cursive Greek chi ≤ 1. In both cases the limit sets are classes of distribution functions, with convergence in the weak topology.

UR - http://www.scopus.com/inward/record.url?scp=0032112296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032112296&partnerID=8YFLogxK

M3 - Article

VL - 34

SP - 545

EP - 563

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 4

ER -