"Non UBC"@en . "DSpace"@en . "Zinsmeister, Michel"@en . "2017-03-21T05:05:07Z"@* . "2016-09-19T11:00"@en . "(Joint work with B.Duplantier, H.Ho and B.Le).\\\n\nIf $f$ is a holomorphic and injective map from the unit disk into the complex plane normalized by $f(0)=0,\,f'(0)=1$ one defines its \"integral means spectrum\" as $p\mapsto \beta_f(p)$ where $\beta_f(p)$ is such that\n$$\int_0^{2\pi}\vert f'(re^{it})\vert^p dt\sim (1-r)^{-\beta_f(p)}$$\nas $r\to 1$. The universal integral means spectrum is the supremum of the set of $\{\beta_f(p)\}$, $f$ over the set of all normalized conformal maps. It is well-known that if we restrict to bounded conformal maps one obtains a different spectrum. The first aim of this talk is to define a generalized integral means spectrum as $(p,q)\mapsto \beta_f(p,q)$ where\n $$\int_0^{2\pi}\frac{\vert f'(re^{it})\vert^p}{\vert f(re^{it})\vert^q} dt\sim (1-r)^{-\beta_f(p,q)}$$\n allowing to unify the bounded/unbounded approach.\\\n We put to use this new concept to study the generalized integral means spectrum of the whole-plane SLE; the case $q=2p$ corresponds to the external (bounded) case studied by Beliaev and Smirnov. There is a gap the latter paper: the proof fails for $p "https://circle.library.ubc.ca/rest/handle/2429/60956?expand=metadata"@en . "48 minutes"@en . "video/mp4"@en . ""@en . "Author affiliation: Universit\u00E9 d' Orl\u00E9ans"@en . "10.14288/1.0343281"@en . "eng"@en . "Unreviewed"@en . "Vancouver : University of British Columbia Library"@en . "Banff International Research Station for Mathematical Innovation and Discovery"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Faculty"@en . "BIRS Workshop Lecture Videos (Oaxaca de Ju\u00E1rez (Mexico))"@en . "Mathematics"@en . "Several complex variables and analytic spaces"@en . "Dynamical systems and ergodic theory"@en . "Classical analysis"@en . "Generalized integral means spectrum of whole-plane SLE"@en . "Moving Image"@en . "http://hdl.handle.net/2429/60956"@en .