@article{c9943585563f4b25b74c9f679ade6763,

title = "A Non-intersecting Random Walk on the Manhattan Lattice and SLE 6 ",

abstract = "We consider a random walk on the Manhattan lattice. The walker must follow the orientations of the bonds in this lattice, and the walker is not allowed to visit a site more than once. When both possible steps are allowed, the walker chooses between them with equal probability. The walks generated by this model are known to be related to interfaces for bond percolation on a square lattice. So it is natural to conjecture that the scaling limit is SLE 6. We test this conjecture with Monte Carlo simulations of the random walk model and find strong support for the conjecture.",

keywords = "Bond percolation, Manhattan lattice, Non-intersecting random walk, Schramm–Loewner evolution",

author = "Tom Kennedy",

note = "Funding Information: Fig. 18 The same differences for the percolation explorer shown in the previous plot are replotted but multiplied by a factor proportional to np with p = 0.24 Acknowledgements An allocation of computer time from the UA Research Computing High Performance Computing (HPC) and High Throughput Computing (HTC) at the University of Arizona is gratefully acknowledged. Funding was provided by Directorate for Mathematical and Physical Sciences (Grant No. DMS-1500850). Funding Information: An allocation of computer time from the UA Research Computing High Performance Computing (HPC) and High Throughput Computing (HTC) at the University of Arizona is gratefully acknowledged. Funding was provided by Directorate for Mathematical and Physical Sciences (Grant No. DMS-1500850). Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

month = jan,

day = "15",

doi = "10.1007/s10955-018-2176-9",

language = "English (US)",

volume = "174",

pages = "77--96",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "1",

}