The glassy phase of complex branching Brownian motion
Madaule, Thomas; Rhodes, Rémi; Vargas, Vincent (2015), The glassy phase of complex branching Brownian motion, Communications in Mathematical Physics, 334, 3, p. 1157-1187. 10.1007/s00220-014-2257-9
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1310.7775v3
Journal nameCommunications in Mathematical Physics
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Abstract (EN)In this paper, we study complex valued branching Brownian motion in the so-called glassy phase, or also called phase II. In this context, we prove a limit theorem for the complex partition function hence confirming a conjecture formulated by Lacoin and the last two authors in a previous paper on complex Gaussian multiplicative chaos. We will show that the limiting partition function can be expressed as a product of a Gaussian random variable, mainly due to the windings of the phase, and a stable transform of the so called derivative martingale, mainly due to the clustering of the modulus. The proof relies on the fine description of the extremal process available in the branching Brownian motion context.
Subjects / Keywordsbranching Brownian motion; glassy phase; freezing
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