caa a22 4500 445390921 CHVBK 20180317143046.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10955-011-0258-z doi (NATIONALLICENCE)springer-10.1007/s10955-011-0258-z The Self-avoiding Walk Spanning a Strip [Elektronische Daten] [Ben Dyhr, Michael Gilbert, Tom Kennedy, Gregory Lawler, Shane Passon] We review the existence of the infinite length self-avoiding walk in the half plane and its relationship to bridges. We prove that this probability measure is also given by the limit as β→β c − of the probability measure on all finite length walks ω with the probability of ω proportional to β |ω| where |ω| is the number of steps in ω. (β c is the reciprocal of the connective constant.) The self-avoiding walk in a strip $\{z : 0<\operatorname{Im}(z)<y\}$ is defined by considering all self-avoiding walks ω in the strip which start at the origin and end somewhere on the top boundary with probability proportional to $\beta_{c}^{|\omega|}$ . We prove that this probability measure may be obtained by conditioning the SAW in the half plane to have a bridge at height y. This observation is the basis for simulations to test conjectures on the distribution of the endpoint of the SAW in a strip and the relationship between the distribution of this strip SAW and SLE8/3. Springer Science+Business Media, LLC, 2011 Self-avoiding walk nationallicence Bridge decomposition nationallicence SLE nationallicence Strip nationallicence Dyhr Ben Metropolitan State College of Denver, Denver, CO, USA aut Gilbert Michael University of Arizona, Tucson, AZ, USA aut Kennedy Tom University of Arizona, Tucson, AZ, USA aut Lawler Gregory University of Chicago, Chicago, IL, USA aut Passon Shane University of Arizona, Tucson, AZ, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/1(2011-07-01), 1-22 0022-4715 144:1<1 2011 144 10955 https://doi.org/10.1007/s10955-011-0258-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0258-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dyhr Ben Metropolitan State College of Denver, Denver, CO, USA aut NATIONALLICENCE 700 1- Gilbert Michael University of Arizona, Tucson, AZ, USA aut NATIONALLICENCE 700 1- Kennedy Tom University of Arizona, Tucson, AZ, USA aut NATIONALLICENCE 700 1- Lawler Gregory University of Chicago, Chicago, IL, USA aut NATIONALLICENCE 700 1- Passon Shane University of Arizona, Tucson, AZ, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/1(2011-07-01), 1-22 0022-4715 144:1<1 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer