| Abstract: |
| The Seiberg bounds form a set of necessary and sufficient conditions under which correlations functions in Liouville conformal field theory are well-defined. Since the probabilistic construction of Liouville correlations functions by David, Kupiainen, Rhodes and Vargas, a probabilistic version of the Seiberg bounds can be obtained via the theory of Gaussian Multiplicative Chaos. We will give a brief review on this construction, and then explain its boundary version, where a new class of Gaussian Multiplicative Chaos emerges naturally. We will discuss finer estimates on the right tail of the Gaussian multiplicative chaos measures if time permits. |
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