共紧紫红色群上的随机漫步

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2013-01-01 DOI:10.24033/ASENS.2186

S. Gouëzel, S. Lalley

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引用次数: 43

摘要

证明了在共紧Fuchsian群上对称有限范围随机游动的Green函数在收敛半径r处随距离呈指数衰减，并证明了ancona不等式等于extendtor，因此r势的martinboundary与自然几何边界s1重合，并且证明了Martin核是一致Holder连续的。最后，给出了跃迁概率的局部极限定理:在非周期情况下，np (x;y) Cx;yR n n 3=2。

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Random walks on co-compact fuchsian groups

It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also shownthatAncona'sinequalitiesextendtoR,andthereforethattheMartinboundaryforR-potentials coincides with the natural geometric boundary S 1 , and that the Martin kernel is uniformly Holder continuous. Finally, this implies a local limit theorem for the transition probabilities: in the aperiodic case, p n (x;y) Cx;yR n n 3=2 .

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.