N-sided radial Schramm-Loewner evolution

被引:5
|
作者
Healey, Vivian Olsiewski [1 ,2 ]
Lawler, Gregory F. [2 ]
机构
[1] Univ Chicago, Chicago, IL 60637 USA
[2] Texas State Univ, Dept Math, San Marcos, TX 78666 USA
关键词
60J67 Stochastic (Schramm-) Loewner Evolution; ERASED RANDOM-WALKS;
D O I
10.1007/s00440-021-01033-9
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We use the interpretation of the Schramm-Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of n-radial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on n-tuples of paths has a limit. The limit measure can be described as n paths moving by the Loewner equation with a driving term of Dyson Brownian motion. While the limit process has been considered before, this paper shows why it naturally arises as a limit of configurational measures obtained from loop measures.
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页码:451 / 488
页数:38
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