caa a22 4500 445391189 CHVBK 20180317143047.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s10955-011-0284-x doi (NATIONALLICENCE)springer-10.1007/s10955-011-0284-x Diaconis Persi Departments of Mathematics and Statistics, Stanford University, Stanford, USA aut The Mathematics of Mixing Things Up [Elektronische Daten] [Persi Diaconis] How long should a Markov chain Monte Carlo algorithm be run? Using examples from statistical physics (Ehrenfest urn, Ising model, hard discs) as well as card shuffling, this tutorial paper gives an overview of a body of mathematical results that can give useful answers to practitioners (viz: seven shuffles suffice for practical purposes). It points to new techniques (path coupling, geometric inequalities, and Harris recurrence). The discovery of phase transitions in mixing times (the cutoff phenomenon) is emphasized. Springer Science+Business Media, LLC, 2011 Markov chains nationallicence Rates of convergence nationallicence Cutoff phenomenon nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/3(2011-08-01), 445-458 0022-4715 144:3<445 2011 144 10955 https://doi.org/10.1007/s10955-011-0284-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0284-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Diaconis Persi Departments of Mathematics and Statistics, Stanford University, Stanford, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/3(2011-08-01), 445-458 0022-4715 144:3<445 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer