Minjae Park

activity

20202023

most citedBrownian loops and the central charge of a Liouville random surface

2 citations · 6 across the 7 of their papers we have counts for

collaborators

7 papers

math.PR2023★ 1 cited

Random surfaces and lattice Yang-Mills

Sky Cao, Minjae Park, Scott Sheffield

We study Wilson loop expectations in lattice Yang-Mills models with a compact Lie group $G$ . Using tools recently introduced in a companion paper, we provide alternate derivations,…

math.PR2023★ 1 cited

Wilson loop expectations as sums over surfaces on the plane

Minjae Park, Joshua Pfeffer, Scott Sheffield +1

Although lattice Yang-Mills theory on finite subgraphs of $Z^{d}$ is easy to rigorously define, the construction of a satisfactory continuum theory on $R^{d}$ is a majo…

math.PR2023

Brownian loops on non-smooth surfaces and the Polyakov-Alvarez formula

Minjae Park, Joshua Pfeffer, Scott Sheffield

Let $ρ$ be compactly supported on $D \subset R^{2}$ . Endow $R^{2}$ with the metric $e^{ρ} (d x_{1}^{2} + d x_{2}^{2})$ . As $δ \to 0$ the set of Brownian loops centered in $D$ with le…

math.PR2022

On the geometry of uniform meandric systems

Jacopo Borga, Ewain Gwynne, Minjae Park

A meandric system of size $n$ is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on ${1, \dots, 2 n}$ , one drawn above the real line and the other bel…

math.PR2022

Loewner evolution driven by complex Brownian motion (with simulations by Minjae Park)

Ewain Gwynne, Joshua Pfeffer

We study the Loewner evolution whose driving function is $W_{t} = B_{t}^{1} + i B_{t}^{2}$ , where $(B^{1}, B^{2})$ is a pair of Brownian motions with a given covariance matrix. This model can be…

math.PR2020★ 2 cited

Brownian loops and the central charge of a Liouville random surface

Morris Ang, Minjae Park, Joshua Pfeffer +1

We explore the geometric meaning of the so-called zeta-regularized determinant of the Laplace-Beltrami operator on a compact surface, with or without boundary. We relate the $(-c/2…

math.PR2020★ 2 cited

Large deviations of radial SLE $_{\infty}$

Morris Ang, Minjae Park, Yilin Wang

We derive the large deviation principle for radial Schramm-Loewner evolution ( $SLE$ ) on the unit disk with parameter $κ \to \infty$ . Restricting to the time i…