{"id":183274,"date":"2006-10-27T00:00:00","date_gmt":"2009-10-31T12:35:49","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/random-sorting-networks\/"},"modified":"2016-09-09T09:47:58","modified_gmt":"2016-09-09T16:47:58","slug":"random-sorting-networks","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/random-sorting-networks\/","title":{"rendered":"Random Sorting Networks"},"content":{"rendered":"<div class=\"asset-content\">\n<p>See http:\/\/www.math.ubc.ca\/~holroyd\/sort for pictures.<\/p>\n<p>Joint work with Omer Angel, Dan Romik and Balint Virag.<\/p>\n<p>Sorting a list of items is perhaps the most celebrated problem in mathematical computer science.  If one must do this by swapping neighboring pairs, the worst initial condition is when the n items are in reverse order, in which case n choose 2 swaps are needed.  A sorting network is any sequence of n choose 2 swaps which achieves this.<\/p>\n<p>We investigate the behavior of a uniformly random n-item sorting network as n -> infinity. We prove a law of large numbers for the space-time process of swaps.  Exact simulations and heuristic arguments have led us to astonishing conjectures.  For example, the half-time permutation matrix appears to be circularly symmetric, while the trajectories of individual items appear to converge to a famous family of smooth curves.  We prove the more modest results that, asymptotically, the support of the matrix lies within a certain octagon, while the trajectories are Holder-1\/2.  A key tool is a connection with Young tableaux.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>See http:\/\/www.math.ubc.ca\/~holroyd\/sort for pictures. Joint work with Omer Angel, Dan Romik and Balint Virag. Sorting a list of items is perhaps the most celebrated problem in mathematical computer science. If one must do this by swapping neighboring pairs, the worst initial condition is when the n items are in reverse order, in which case n [&hellip;]<\/p>\n","protected":false},"featured_media":194977,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-183274","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/eLNEqQjJbao","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/183274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/183274\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/194977"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=183274"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=183274"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=183274"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=183274"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=183274"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=183274"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=183274"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=183274"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=183274"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=183274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}