BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//6.4.7.2//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:0-1140@lptms.universite-paris-saclay.fr DTSTART;TZID=Europe/Paris:20260626T150000 DTEND;TZID=Europe/Paris:20260626T173000 DTSTAMP:20260612T145552Z URL:https://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-th ese-maximilien-bernard/ SUMMARY:Soutenance de thèse Maximilien Bernard - LPENS Paris - 26 Juin 26 15:00 DESCRIPTION:Fluctuations and multifractality in stochastic models of interf ace growth and population dynamics\n \;\nMaximilien Bernard\n \;\n \nLieu de la soutenance : LPENS\, 24 Rue Lhomond\, 75005\, Paris\, salle C onf IV\n\n\nThis thesis studies how disorder and fluctuations shape large- scale growth phenomena in three related settings: fluctuating interfaces\, random spring chains\, and random multiplicative growth. The first part c oncerns interface growth. In standard kinetic roughening\, an initially fl at interface becomes rough and develops correlations over increasing lengt h scales. This behavior is characterized by scaling exponents\, which desc ribe how height fluctuations grow in space and time. These exponents can b e measured either through global observables\, probing the whole interface \, or through local observables restricted to a finite window. In many exp erimental and numerical systems\, however\, these two descriptions do not agree\, a phenomenon known as anomalous scaling. To clarify its origin\, w e study two models in which this mismatch has different causes. The first is a heterogeneous elastic line\, where we show that the apparent anomaly is a purely statistical effect. The second is the stochastic porous medium equation\, a strongly nonlinear model in which the anomaly is genuine: th e interfaces display distinct local and global laws that we determine. The second part concerns Anderson localization\, which appears here through t he spectral properties of the heterogeneous elastic lines. In a homogeneou s chain\, vibrational eigenmodes are extended over the whole system. In th e presence of quenched disorder\, they may instead become spatially locali zed\, with amplitudes concentrated near a localization center and decaying away from it. We study chains with both random masses and random spring c onstants\, with particular emphasis on the strong-disorder regime\, where standard weak-disorder expansions break down. We develop a new combinatori al method to probe this regime. The last part concerns random multiplicati ve growth with redistribution. In such models\, changes in wealth\, popula tion\, or mass\, for instance\, are proportional to the amount already pre sent\, so that small differences are amplified over time. This naturally g enerates broad distributions and provides a simple mechanism for the emerg ence of inequality and concentration\, with applications to population dyn amics\, wealth distribution\, city growth\, and ecology. We in particular study models in which each site has its own quenched growth rate\, represe nting a persistent advantage or disadvantage\, and is also subject to tran sient fluctuations. Redistribution competes with these mechanisms by homog enizing the system. This competition leads to rich phase diagrams\, with l ocalized and delocalized phases\, as well as a new intermediate phase\, wh ich we call partially localized\, and which arises from the interplay betw een quenched heterogeneity and temporal noise.\n\nJury: Yan Fyodorov\, Pie rre Le Doussal (directeur de thèse)\, Cécile Monthus\, Romualdo Pastor S atorras\, Aleksandra Petkovic\, Alberto Rosso (co-directeur de thèse)\, S tefano Zapperi CATEGORIES:seminars LOCATION:LPENS Paris\, 24 Rue Lhomond\, Paris\, 75005\, France X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=24 Rue Lhomond\, Paris\, 75 005\, France;X-APPLE-RADIUS=100;X-TITLE=LPENS Paris:geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20260329T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR