Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	钱玮博士，香港城市大学数学系
Inviter:
Title:	Conformally invariant fields out of Brownian loop soups
Language:	Chinese
Time & Venue:	2023.03.29 14:00-15:30 Zoom会议号：869 3063 0661 N620
Abstract:	For each central charge c\in (0,1], we construct a conformally invariant field which is a measurable function of the local time field \mathcal{L} of the Brownian loop soup with intensity c and i.i.d. signs given to each cluster. This field is canonically associated to $\mathcal{L}$, in a sense which is similar to the isomorphism theory that associates the Gaussian free field to the loop soup with critical intensity. Isomorphisms between Brownian motions and random fields were previously developed by Symanzik, Brydges-Fr鰄lich-Spencer, Dynkin and Le Jan in several different settings. In a key intermediate step, we obtain the crossing exponent for the event that a cluster in the subcritical loop soup passes near a given point. Among other things, it allows us to deduce that the Minkowski gauge function of a cluster in a loop soup with intensity c\in (0,1), which is t^2 f(t) for some f(t)=\|\log t\|^{1-c/2+o(1)}. I will also present several conjectures about this family of fields. This talk is based on joint works with Antoine Jego (EPFL) and Titus Lupu (CNRS).