A fast algorithm for simulating the chordal Schramm-Loewner Evolution

Tom Kennedy

doi:10.1007/s10955-007-9358-1

A fast algorithm for simulating the chordal Schramm-Loewner Evolution

Tom Kennedy

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into N subintervals and approximating the random conformal map of the SLE by the composition of N random, but relatively simple, conformal maps. In the usual implementation the time required to compute a single point on the SLE curve is O(N). We give an algorithm for which the time to compute a single point is O(N ^p ) with p<1. Simulations with κ=8/3 and κ=6 both give a value of p of approximately 0.4.

Original language	English (US)
Pages (from-to)	1125-1137
Number of pages	13
Journal	Journal of Statistical Physics
Volume	128
Issue number	5
DOIs	https://doi.org/10.1007/s10955-007-9358-1
State	Published - Sep 2007

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1007/s10955-007-9358-1

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title = "A fast algorithm for simulating the chordal Schramm-Loewner Evolution",

abstract = "The Schramm-Loewner evolution (SLE) can be simulated by dividing the time interval into N subintervals and approximating the random conformal map of the SLE by the composition of N random, but relatively simple, conformal maps. In the usual implementation the time required to compute a single point on the SLE curve is O(N). We give an algorithm for which the time to compute a single point is O(N p ) with p<1. Simulations with κ=8/3 and κ=6 both give a value of p of approximately 0.4.",

author = "Tom Kennedy",

note = "Funding Information: Fig. 10 Time per point computed as a function of N. The four curves correspond to n = 8↪ 10↪ 12↪ 14. The line shown has slope 0.4 (color online) Acknowledgements The Banff International Research Station made possible many fruitful interactions. In particular, I learned much of the material in Sect. 2 from conversations with Steffen Rohde and Don Marshall. This work was supported by the National Science Foundation (DMS-0201566 and DMS-0501168).",

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doi = "10.1007/s10955-007-9358-1",

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N1 - Funding Information: Fig. 10 Time per point computed as a function of N. The four curves correspond to n = 8↪ 10↪ 12↪ 14. The line shown has slope 0.4 (color online) Acknowledgements The Banff International Research Station made possible many fruitful interactions. In particular, I learned much of the material in Sect. 2 from conversations with Steffen Rohde and Don Marshall. This work was supported by the National Science Foundation (DMS-0201566 and DMS-0501168).

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A fast algorithm for simulating the chordal Schramm-Loewner Evolution

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