We consider regularized versions of the stochastic heat equation (SHE) in high dimensions $d\\geq 3$ and analyze their higher moments in the limit as the regularization is removed, for varying coupling constants that describe the strength of the driving noise. Motivated by recent results on the higher moments of the SHE in two dimensions at $L^{2}$-criticality, a natural question is whether the higher moments of the SHE in high dimensions also converge at the $L^{2}$-critical point. Our main result gives a negative answer: in high dimensions, the higher moments diverge when the coupling constant belongs to a nontrivial right-closed interval whose upper endpoint is the $L^{2}$-critical point. In particular, we obtain a sharp bound for the critical coupling constant at which the corresponding limiting higher moment undergoes a phase transition. As an application to the continuous directed polymer, we derive a sharp estimate for quantity believed to be closely related to the tail probability of the limiting partition function.
","image_description":"","creation_date":"2025-09-12T13:47:07","last_modification_date":"2026-03-30T15:59:29","link_label":"Working-Reading Seminar","link_url":"https://www.epfl.ch/labs/stoan/reading-working-seminar/","canceled":"False","cancel_reason":"","place_and_room":"MA B2 485","url_place_and_room":"","url_online_room":"","spoken_languages":["https://memento.epfl.ch/api/v1/spoken_languages/2/?format=json"],"speaker":"Dr Te-Chun Wang (EPFL)","organizer":" Xue-Mei Li","contact":"Xue-Mei Li","is_internal":"False","theme":"","vulgarization":{"id":3,"fr_label":"Expert","en_label":"Expert"},"registration":{"id":3,"fr_label":"Entrée libre","en_label":"Free"},"keywords":"Reading-Working Seminar","file":null,"icalendar_url":"https://memento.epfl.ch/event/export/117635/","category":{"id":1,"code":"CONF","fr_label":"Conférences - Séminaires","en_label":"Conferences - Seminars","activated":true},"academic_calendar_category":null,"domains":[],"mementos":["https://memento.epfl.ch/api/v1/mementos/1/?format=json","https://memento.epfl.ch/api/v1/mementos/403/?format=json","https://memento.epfl.ch/api/v1/mementos/7/?format=json","https://memento.epfl.ch/api/v1/mementos/6/?format=json"]},{"id":71172,"title":"Anisotropic Inviscid Limit for the Navier-Stokes Equations with Transport Noise Between Two Plates","slug":"anisotropic-inviscid-limit-for-the-navier-stokes-e","event_url":"https://memento.epfl.ch/event/anisotropic-inviscid-limit-for-the-navier-stokes-e","visual_url":"https://memento.epfl.ch/image/32540/200x112.jpg","visual_large_url":"https://memento.epfl.ch/image/32540/720x405.jpg","visual_maxsize_url":"https://memento.epfl.ch/image/32540/max-size.jpg","lang":"en","start_date":"2026-03-24","end_date":"2026-05-25","start_time":"16:30:00","end_time":"17:30:00","description":"We investigate an anisotropic vanishing viscosity limit of the 3D stochastic Navier-Stokes equations posed between two horizontal plates, with Dirichlet no-slip boundary condition. The turbulent viscosity is split into horizontal and vertical directions, each of which approaches zero at a different rate. The underlying Cylindrical Brownian Motion driving our transport-stretching noise is decomposed into horizontal and vertical components, which are scaled by the square root of the respective directional viscosities. We prove that if the ratio of the vertical to horizontal viscosities approaches zero, then there exists a sequence of weak martingale solutions convergent to the strong solution of the deterministic Euler equation on its lifetime of existence. A particular challenge is that the anisotropic scaling ruins the divergence-free property for the spatial correlation functions of the noise.
","image_description":"","creation_date":"2026-02-18T12:59:24","last_modification_date":"2026-03-22T19:58:56","link_label":"Working-Reading Seminar","link_url":"https://www.epfl.ch/labs/stoan/reading-working-seminar/","canceled":"True","cancel_reason":"","place_and_room":"MA B2 485","url_place_and_room":"","url_online_room":"","spoken_languages":["https://memento.epfl.ch/api/v1/spoken_languages/2/?format=json"],"speaker":"Dr Daniel Goodair (EPFL)","organizer":"Xue-Mei Li","contact":"Xue-Mei Li","is_internal":"False","theme":"","vulgarization":{"id":3,"fr_label":"Expert","en_label":"Expert"},"registration":{"id":3,"fr_label":"Entrée libre","en_label":"Free"},"keywords":"Working-Reading seminar, Probability, stochastic analysis","file":null,"icalendar_url":"https://memento.epfl.ch/event/export/119781/","category":{"id":1,"code":"CONF","fr_label":"Conférences - Séminaires","en_label":"Conferences - Seminars","activated":true},"academic_calendar_category":null,"domains":[],"mementos":["https://memento.epfl.ch/api/v1/mementos/7/?format=json"]},{"id":71566,"title":"Climate Launchpad 2026","slug":"climate-launchpad-2026","event_url":"https://memento.epfl.ch/event/climate-launchpad-2026","visual_url":"https://memento.epfl.ch/image/32902/200x112.jpg","visual_large_url":"https://memento.epfl.ch/image/32902/720x405.jpg","visual_maxsize_url":"https://memento.epfl.ch/image/32902/max-size.jpg","lang":"en","start_date":"2026-05-15","end_date":"2026-05-15","start_time":"11:00:00","end_time":"12:00:00","description":"Do you have a sustainable business idea? Start here – ClimateLaunchpad 2026The Swiss startup days (SUD) are the leading deep-tech catalyst event where Switzerland’s innovation bridges are built.
\r\n
\r\nFrom mindset to connection to action, SUD empowers entrepreneurs, investors, corporates, and enablers to create a stronger, more connected, and more resilient startup ecosystem - all in a single day.
\r\n
\r\nOn 21 May 2026, the entire ecosystem comes together for a full day of keynotes, sessions, and startup pitches, plus 1:1 meetings, a buzzing exhibition area, and 1,500 participants ready to exchange ideas, insights, and opportunities.
\r\n
\r\nBe part of the catalyst event to accelerate your innovation journey.
\r\n
\r\nFree tickets (limited to EPFL Startups and first come first serve) - contact Aurelie
\r\n
\r\nCome and meet the startups at EPFL Innovation Park!
\r\nA unique and hands-on opportunity to discover startups' activities, meet their founders and network !
\r\n
\r\nA casual but stimulating opportunity to mingle with other participants, discuss innovative ideas and enjoy slices of pizzas in a relaxed atmosphere. It's the ideal setting for making new contacts and discovering the startups at EPFL Innovation Park.
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\r\nThe conference takes place at at EPFL Innovation Park (Room Uranus, building D) during lunchtime. Pizzas will be served after the presentations.
\r\nParticipation is free but registration is mandatory.
\r\n
\r\nAgenda\r\n
Thesis Directors: Prof. G. Boero, Dr H. Furci
\r\nMicrosystems and Microelectronics doctoral program
\r\nThesis Nr. 11256
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\r\nTo take part in the public defense, please contact directly the speaker