Schramm-Loewner Evolution Library

schramm_loewner_evolution is a package that brings in Python the wonderful theory of Single and Multiple Schramm-Loewner Evolution!

About

While staying at the Department of Mathematics of the University of Rome "Tor Vergata", Andrea del Monaco and Sebastian Schleißinger were working on the behavior of multiple SLEs as the number of slits approches infinity.
In order to confirm their guesses, they had the insight of implenting their results in a Python package. This allowed them to simulate such an evolution in many different contexts, and it validated empirically their ideas.

They ended up with writing two papers (the second one in cooperation with Ikkei Hotta):

• A.del Monaco and S.Schleißinger, "Multiple SLE and the complex Burgers equation". Math. Nachr. (2016), 289: 2007–2018. doi:10.1002/mana.201500230
• A.del Monaco, I.Hotta, and S.Schleißinger, "Tightness Results for Infinite-Slit Limits of the Chordal Loewner Equation". S. Comput. Methods Funct. Theory (2018) 18: 9. doi:10.1007/s40315-017-0205-3

It is worth mentioning that the numerical methods for evolution computations are based on:

• T.Kennedy, "Numerical Computations for the Schramm-Loewner Evolution", J. Stat. Phys (2009) 137: 839. doi:10.1007/s10955-009-9866-2

Requirements

schramm_loewner_evolution has only been tested to work on Python >= 3.6
and it depends on

• numpy >= 1.15.1
• numexpr >= 2.6.6

Furthermore, the following packages are required:

• sdeint >= 0.2.2-dev

Any help to check compatibility with Python == 2.x is welcome and encouraged as well as very much appreciated!

Change Log

Spring, 2016
   Version 0.0.1
     First release