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| Content Provider | Springer Nature Link |
|---|---|
| Author | Jokela, Niko Järvinen, Matti Kytölä, Kalle |
| Copyright Year | 2015 |
| Abstract | We study the probabilities with which chordal Schramm–Loewner evolutions (SLE) visit small neighborhoods of boundary points. We find formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary zig-zags or order refined SLE multi-point Green’s functions on the boundary. Remarkably, an exact answer can be found to this important SLE question for an arbitrarily large number of marked points. The main technique employed is a spin chain–Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko–Fateev type integrals. We show how to express these integral formulas in terms of regularized real integrals, and we discuss their numerical evaluation. The results are universal in the sense that apart from an overall multiplicative constant the same formula gives the amplitude for many different formulations of the SLE boundary visit problem. The formula also applies to renormalized boundary visit probabilities for interfaces in critical lattice models of statistical mechanics: we compare the results with numerical simulations of percolation, loop-erased random walk, and Fortuin–Kasteleyn random cluster models at Q = 2 and Q = 3, and find good agreement. |
| Starting Page | 1263 |
| Ending Page | 1330 |
| Page Count | 68 |
| File Format | |
| ISSN | 14240637 |
| Journal | Annales Henri Poincaré |
| Volume Number | 17 |
| Issue Number | 6 |
| e-ISSN | 14240661 |
| Language | English |
| Publisher | Springer International Publishing |
| Publisher Date | 2015-12-19 |
| Publisher Place | Cham |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Theoretical, Mathematical and Computational Physics Dynamical Systems and Ergodic Theory Quantum Physics Mathematical Methods in Physics Classical and Quantum Gravitation, Relativity Theory Elementary Particles, Quantum Field Theory |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistical and Nonlinear Physics Nuclear and High Energy Physics Mathematical Physics |
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