Asymptotic Properties of Some Random Evolutions and Geometries
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Author | : Alexander Joseph Dunlap |
Publisher | : |
Total Pages | : |
Release | : 2020 |
ISBN-10 | : OCLC:1190756241 |
ISBN-13 | : |
Rating | : 4/5 (41 Downloads) |
Book Synopsis Asymptotic Properties of Some Random Evolutions and Geometries by : Alexander Joseph Dunlap
Book excerpt: This thesis comprises two parts. The first part concerns asymptotic properties of the stochastic heat, Kardar--Parisi--Zhang, and Burgers equations, as well as the fractional parabolic Anderson model. We show several results about long-time behavior and scaling limits of these equations. The second part concerns the Liouville quantum gravity metric. We show the existence of subsequential scaling limits of two natural regularizations of this metric, in the first case at very high temperature and in the second case for all subcritical temperatures.