{"id":1751,"date":"2021-05-03T12:59:58","date_gmt":"2021-05-03T10:59:58","guid":{"rendered":"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/"},"modified":"2025-03-06T16:36:55","modified_gmt":"2025-03-06T15:36:55","slug":"the-percolation-phase-transition-of-the-random-plane-wave","status":"publish","type":"events","link":"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/","title":{"rendered":"The percolation phase transition of the random plane wave"},"content":{"rendered":"\n<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\">\n<p><strong>Abstract: <\/strong>Consider the random plane wave f, which is a random eigenfunction of the Laplacian in R^2. Given a real number u, we study the connectivity properties of the set {f<u}, and we show that the model undergoes a percolation phase transition at u=0: if u<0 then a.s. there is no unbounded connected component in {f<u} while this is a.s. the case if u>0. As I will explain in the talk, the main difficulty is that the field is not positively correlated. In the talk, I will present the strategy of proof, based on some superconcentration considerations that have enabled us to revisit the following general idea from (Russo, 1982; Talagrand, 1994&#8230;): \u00ab\u00a0an event satisfies a phase transition if it depends little on any given point\u00a0\u00bb. This is joint work with Stephen Muirhead and Alejandro Rivera<\/p>\n\n\n\n<p>Webex meeting information:<\/p>\n\n\n\n<p><a href=\"https:\/\/unilu.webex.com\/unilu\/j.php?MTID=mc5d4abd209d27a50440fe2a76eaf72b3\" target=\"_self\" title=\"\" rel=\"noopener\">https:\/\/unilu.webex.com\/unilu\/j.php?MTID=mc5d4abd209d27a50440fe2a76eaf72b3<\/a><\/p>\n\n\n\n<p>Thursday, May 6, 2021 1:00 pm | 1 hour | (UTC+02:00) Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna<\/p>\n\n\n\n<p>Meeting number: 163 304 7008<\/p>\n\n\n\n<p>Password: cPP6diqPK74<\/p>\n<\/div><\/section>\n","protected":false},"excerpt":{"rendered":"<p>Abstract: Consider the random plane wave f, which is a random eigenfunction of the Laplacian in R^2. Given a real number u, we study the connectivity properties of the set {f&lt;u}, and we show that the model undergoes a percolation phase transition at u=0: if u&lt;0 then a.s. there is no unbounded connected component in {f&lt;u} while this is a.s. the case if u&gt;0. As I will explain in the talk, the main difficulty is that the field is not positively correlated. In the talk, I will present the strategy of proof, based on some superconcentration considerations that have enabled us to revisit the following general idea from (Russo, 1982; Talagrand, 1994&#8230;): \u00ab\u00a0an event satisfies a phase transition if it depends little on any given point\u00a0\u00bb. This is joint work with Stephen Muirhead and Alejandro Rivera<\/p>\n","protected":false},"author":44,"featured_media":1752,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","format":"standard","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"","uluxPrePostTitle":"","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"event_start_date":"2021-05-06 13:00:00","event_end_date":"2021-05-06 18:00:00","event_speaker_name":"Hugo Vanneuville from Universit\u00e9 Grenoble-Alpes","event_speaker_link":"","event_is_online":false,"event_location":"WEBEX","event_street":".","event_location_link":"","event_zip_code":".","event_city":".","event_country":"LU"},"events-topic":[309],"events-type":[],"organisation":[60],"authorship":[44],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The percolation phase transition of the random plane wave - FSTM I Uni.lu<\/title>\n<meta name=\"description\" content=\"Abstract: Consider the random plane wave f, which is a random eigenfunction of the Laplacian in R^2. Given a real number u, we study the connectivity properties of the set {f&lt;u}, and we show that the model undergoes a percolation phase transition at u=0: if u&lt;0 then a.s. there is no unbounded connected component in {f&lt;u} while this is a.s. the case if u&gt;0. As I will explain in the talk, the main difficulty is that the field is not positively correlated. In the talk, I will present the strategy of proof, based on some superconcentration considerations that have enabled us to revisit the following general idea from (Russo, 1982; Talagrand, 1994...): &quot;an event satisfies a phase transition if it depends little on any given point&quot;. This is joint work with Stephen Muirhead and Alejandro Rivera\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The percolation phase transition of the random plane wave\" \/>\n<meta property=\"og:description\" content=\"Abstract: Consider the random plane wave f, which is a random eigenfunction of the Laplacian in R^2. Given a real number u, we study the connectivity properties of the set {f&lt;u}, and we show that the model undergoes a percolation phase transition at u=0: if u&lt;0 then a.s. there is no unbounded connected component in {f&lt;u} while this is a.s. the case if u&gt;0. As I will explain in the talk, the main difficulty is that the field is not positively correlated. In the talk, I will present the strategy of proof, based on some superconcentration considerations that have enabled us to revisit the following general idea from (Russo, 1982; Talagrand, 1994...): &quot;an event satisfies a phase transition if it depends little on any given point&quot;. This is joint work with Stephen Muirhead and Alejandro Rivera\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/\" \/>\n<meta property=\"og:site_name\" content=\"FSTM FR\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/fstm.uni.lu\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-03-06T15:36:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/20\/2021\/05\/default.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1500\" \/>\n\t<meta property=\"og:image:height\" content=\"1125\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/\",\"url\":\"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/\",\"name\":\"The percolation phase transition of the random plane wave - FSTM I Uni.lu\",\"isPartOf\":{\"@id\":\"https:\/\/www.uni.lu\/fstm-fr\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.uni.lu\/fstm-fr\/events\/the-percolation-phase-transition-of-the-random-plane-wave\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/20\/2021\/05\/default.jpg\",\"datePublished\":\"2021-05-03T10:59:58+00:00\",\"dateModified\":\"2025-03-06T15:36:55+00:00\",\"description\":\"Abstract: Consider the random plane wave f, which is a random eigenfunction of the Laplacian in R^2. 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