Three phases of multiple SLE driven by non-colliding Dyson's Brownian motions

Makoto Katori, Shinji Koshida*

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

Abstrakti

The present paper is concerned with properties of multiple Schramm-Loewner evolutions (SLEs) labelled by a parameter kappa is an element of (0, 8]. Specifically, we consider the solution of the multiple Loewner equation driven by a time change of Dyson's Brownian motions in the non-colliding regime. Although it is often considered that several properties of the solution can be studied by means of commutation relations of SLEs and the absolute continuity, this method is available only in the case that the curves generated by commuting SLEs are separated. Beyond this restriction, it is not even obvious that the solution of the multiple Loewner equation generates multiple curves. To overcome this difficulty, we employ the coupling of Gaussian free fields and multiple SLEs. Consequently, we prove the longstanding conjecture that the solution indeed generates multiple continuous curves. Furthermore, these multiple curves are (i) simple disjoint curves when kappa is an element of (0, 4], (ii) intersecting curves when kappa is an element of (4, 8), and (iii) space-filling curves when kappa = 8.

AlkuperäiskieliEnglanti
Artikkeli325002
Sivumäärä19
JulkaisuJournal of Physics A: Mathematical and Theoretical
Vuosikerta54
Numero32
DOI - pysyväislinkit
TilaJulkaistu - 13 elokuuta 2021
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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