Stochastc Komatu–Loewner Evolutons

Zhen-Qing Chen

University of Washington, USA

Masatoshi Fukushima Osaka University, Japan

Key Features

Takuya Murayama Kyushu University, Japan

• his book gives a s stematc e tension o the mathematcal theor o Schramm Loewner evoluton (SLE) to multpl connected planar domains, namel , domains allowing fnitel man holes

• opics are presented in a unifed and mostl sel contained manner, accessible b interested researchers and graduate students

• rownian moton with darning ( ) and stochastc anal sis are utli ed in an essental wa in the stud o con ormal mappings and Komatu Loewner evolutons on multpl connected planar domains

Descripton

The present monograph on stochastc Komatu–Loewner evolutons (SKLEs) provides the frst systematc extension of the Schramm–Loewner evoluton (SLE) theory from a simply connected planar domain to multply connected domains by using the Brownian moton with darning (BMD) that has arisen in a recent study of the boundary theory of symmetric Markov processes.

his volume is presented in an accessible manner or the interested researchers and graduate students. t also brings new insights into SLEs as special cases o SKLEs. athematcall , it can be viewed as a power ul applicaton o stochastc anal sis via s to comple anal sis.

Authors

Zhen-Qing Chen is a pro essor at the Universit o Washington, US . He is an elected ellow o the merican athematcal Societ and o the nsttute o athematcal Statstcs. He has co authored with ukushima on the book S mmetric arkov Processes, ime Changes, and oundar heor . He serves on several editorial boards o mathematcal research ournals, including Potental nal sis as the Editor in Chie .

Masatoshi Fukushima is a Pro essor Emeritus at the saka Universit , apan. He is well known or his undamental contributons in irichlet orm theor . He is an author o three books on irichlet orm theor . He received the 2003 nal sis Pri e rom the athematcal Societ o apan, and the 20 9 t Pri e (together with Chen) rom the ernoulli Societ .

Since pril 2022, Takuya Murayama is ssistant Pro essor at K ushu Universit , apan.

January 2023

Imprint: World Scientfc Publishing Compan

Extent: 252pp

Type: onograph

Main Subject: athematcs

Sub-Subjects: Probabilit heor

Stochastc Processes unctons

Comple ariable rdinar i erental E uatons Partal i erental E uaton

Statstcal Ph sics, Comple it and onlinear namical S stems ( ncluding Heat nd hermod namics)

Keywords: bsorbed rownian oton

( ) rownian oton with arning ( ) Comple Poisson Kernel

Komatu Loewner i erental E uaton

Hulls Canonical ap Hal Plane

Capacit K L E uaton or Slit otons

Komatu Loewner Evoluton (KLE)

Stochastc Komatu Loewner Evoluton (SKLE) omain arkov Propert

Contnuousl Growing Hulls riving uncton omain Constant

Readership: esearchers and graduate students interested in the Schramm Loewner evoluton (SLE)

• ultpl Connected Planar omain and rownian oton

• Chordal Komatu Loewner i erental E uaton and

• Komatu Loewner Evoluton (KLE)

• Stochastc Komatu Loewner Evoluton (SKLE)

• KLE and its rans ormaton

• Appendix