arXiv:2006.13767v3 [math.PR] 2 Jul 2020 Page 1 arXiv:2006.13767v3 [math.PR] 2 Jul 2020
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …

Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in
which the problem was reduced to the study of certain" random surfaces". He further made …

Consider a Brownian loop soup $\mathcal {L} _D^\theta $ with subcritical intensity $\theta\in
(0, 1/2] $ in some 2D bounded simply connected domain. We define and study the …

We characterise the multiplicative chaos measure M associated to planar Brownian motion
introduced in Bass et al.(Ann Probab 22 (2): 566–625, 1994), Aïdékon et al.(Ann. Probab. 48 …

We construct the analogue of Gaussian multiplicative chaos measures for the local times of
planar Brownian motion by exponentiating the square root of the local times of small circles …

We construct a measure on the thick points of a Brownian loop soup in a bounded domain
DD of the plane with given intensity θ> 0 θ>0, which is formally obtained by exponentiating …

The aim of this paper is to present a self-similar growth-fragmentation process linked to a
Brownian excursion in the upper half-plane H, obtained by cutting the excursion at …

Brownian multiplicative chaos measures, introduced in Jego (Ann Probab 48: 1597–1643,
2020), Aïdékon et al.(Ann Probab 48 (4): 1785–1825, 2020) and Bass et al.(Ann Probab 22 …

We consider a continuous-time random walk on a regular tree of finite depth and study its
favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped …

We study percolation of two-sided level sets for the discrete Gaussian free field (DGFF) in
2D. For a DGFF $\varphi $ defined in a box $ B_N $ with side length $ N $, we show that …