caa a22 4500 46789177X CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10955-006-9132-9 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9132-9 Dubédat Julien Courant Institute of Mathematical Sciences, 251 Mercer St., 10012, New York, USA aut Euler Integrals for Commuting SLEs [Elektronische Daten] [Julien Dubédat] Schramm-Loewner Evolutions (SLEs) have proved an efficient way to describe a single continuous random conformally invariant interface in a simply-connected planar domain; the admissible probability distributions are parameterized by a single positive parameter κ. As shown in, Ref. 8 the coexistence of n interfaces in such a domain implies algebraic ("commutation”) conditions. In the most interesting situations, the admissible laws on systems of n interfaces are parameterized by κ and the solution of a particular (finite rank) holonomic system. The study of solutions of differential systems, in particular their global behaviour, often involves the use of integral representations. In the present article, we provide Euler integral representations for solutions of holonomic systems arising from SLE commutation. Applications to critical percolation (general crossing formulae), Loop-Erased Random Walks (direct derivation of Fomin's formulae in the scaling limit), and Uniform Spanning Trees are discussed. The connection with conformal restriction and Poissonized non-intersection for chordal SLEs is also studied. Springer Science + Business Media, Inc., 2006 correlation functions nationallicence critical percolation nationallicence Schramm-loewner evolutions nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1183-1218 0022-4715 123:6<1183 2006 123 10955 https://doi.org/10.1007/s10955-006-9132-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9132-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dubédat Julien Courant Institute of Mathematical Sciences, 251 Mercer St., 10012, New York, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1183-1218 0022-4715 123:6<1183 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer