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            "title": "Mathematics Colloquium",
            "slug": "mathematics-colloquium-13",
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            "start_date": "2026-06-17",
            "end_date": "2026-06-17",
            "start_time": "16:15:00",
            "end_time": "17:15:00",
            "description": "<strong>Title</strong>: <br>\r\nPositive random walks and positive-semidefinite random matrices<br>\r\n<br>\r\n<strong>Abstract</strong>:<br>\r\nOn the real line, a random walk that can only move in the positive direction is very unlikely to remain close to its origin. After a fixed number of steps, the left tail has a Gaussian profile under minimal assumptions. Remarkably, a similar phenomenon occurs when we consider a positive random walk on the cone of positive-semidefinite matrices. After a fixed number of steps, the minimum eigenvalue is described by a Gaussian random matrix model.<br>\r\nThis talk introduces a new way to make this intuition rigorous. The methodology addresses an open problem in computational mathematics about sparse random embeddings. The presentation targets a general mathematical audience.<br>\r\nPreprint: <a href=\"https://arxiv.org/abs/2501.16578\" target=\"_blank\">https://arxiv.org/abs/2501.16578</a><br>\r\n<br>\r\n<strong>Please register on the following form : </strong>https://forms.gle/ppXwKo9HmTgFk3rc7",
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            "creation_date": "2026-04-01T11:03:30",
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            "speaker": "Prof. Joel A. Tropp, Steele Family Professor of Applied &amp; Computational Mathematics, Caltech",
            "organizer": "Prof. Nicolas Boumal",
            "contact": "Institute of Mathematics",
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