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            "id": 69803,
            "title": "Higher moments for the SHE in high dimensions and their phase transitions",
            "slug": "higher-moments-for-the-she-in-high-dimensions-and",
            "event_url": "https://memento.epfl.ch/event/higher-moments-for-the-she-in-high-dimensions-and",
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            "lang": "en",
            "start_date": "2026-04-14",
            "end_date": "2026-04-15",
            "start_time": "10:10:00",
            "end_time": "11:00:00",
            "description": "<p>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.</p>",
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            "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/",
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            "speaker": "Dr Te-Chun Wang (EPFL)",
            "organizer": " <a href=\"https://people.epfl.ch/xue-mei.li\">Xue-Mei Li</a>",
            "contact": "<a href=\"https://people.epfl.ch/xue-mei.li\">Xue-Mei Li</a>",
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            "keywords": "Reading-Working  Seminar",
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