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 the past 25 years, there has been an explosion of interest in the area of random tilings.
The first book devoted to the topic, this timely text describes the mathematical theory of …

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 …

Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal
surfaces which first appeared in the physics literature in the 1980s. Recent works have …

We show that for each c M∈ 1, 25) c_M∈1,25), there is a unique metric associated with
Liouville quantum gravity (LQG) with matter central charge c M c_M. An earlier series of …

Generative models based on denoising diffusion techniques have led to an unprecedented
increase in the quality and diversity of imagery that is now possible to create with neural …

It is believed that Euclidean Yang–Mills theories behave like the massless Gaussian free
field (GFF) at short distances. This makes it impossible to define the main observables for …

We prove that the simple random walk on the uniform infinite planar triangulation (UIPT)
typically travels graph distance at most n^ 1/4+ o_n (1) n 1/4+ on (1) in n units of time …

We define a random metric associated to Liouville quantum gravity (LQG) for all values of
matter central charge c< 2 5 by extending the axioms for a weak LQG metric from the c< 1 …

Liouville first passage percolation (LFPP) with parameter> 0 is the family of random distance
functions ¹Dhº> 0 on the plane obtained by integrating eh along paths, where h for> 0 is a …