Joshua Pfeffer

activity

20142024

most citedLiouville quantum gravity with matter central charge in

(1, 25)

: a probabilistic approach

16 citations · 28 across the 12 of their papers we have counts for

collaborators

14 papers

cs.SD2024

Mathematics of the MML functional quantizer modules for VCV Rack software synthesizer

Maxwell Schneider, Cody McCarthy, Michael G. Maxwell +3

We detail the mathematical formulation of the line of "functional quantizer" modules developed by the Mathematics and Music Lab (MML) at Michigan Technological University, for the…

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

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.PR2021★ 2 cited

Weak Liouville quantum gravity metrics with matter central charge $c \in (- \infty, 25)$

Joshua Pfeffer

Physics considerations suggest that a theory of Liouville quantum gravity (LQG) should exist for all values of matter central charge $c \in (- \infty, 25)$ . Probabilists hav…

math.PR2020

Geodesics and metric ball boundaries in Liouville quantum gravity

Ewain Gwynne, Joshua Pfeffer, Scott Sheffield

Recent works have shown that there is a canonical way to to assign a metric (distance function) to a Liouville quantum gravity (LQG) surface for any parameter $γ \in (0, 2)$ . We esta…

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.PR2019

KPZ formulas for the Liouville quantum gravity metric

Ewain Gwynne, Joshua Pfeffer

Let $γ \in (0, 2)$ , let $h$ be the planar Gaussian free field, and let $D_{h}$ be the associated $γ$ -Liouville quantum gravity (LQG) metric. We prove that for any random Borel set $X \…

math.PR2019

Weak LQG metrics and Liouville first passage percolation

Julien Dubédat, Hugo Falconet, Ewain Gwynne +2

For $γ \in (0, 2)$ , we define a weak $γ$ -Liouville quantum gravity (LQG) metric to be a function $h \mapsto D_{h}$ which takes in an instance of the planar Gaussian free field (GFF) and…

math.PR2019

Bounds for distances and geodesic dimension in Liouville first passage percolation

Ewain Gwynne, Joshua Pfeffer

For $ξ \geq 0$ , Liouville first passage percolation (LFPP) is the random metric on $ε Z^{2}$ obtained by weighting each vertex by $ε e^{ξ h_{ε} (z)}$ …

math.PR2019★ 16 cited

Liouville quantum gravity with matter central charge in $(1, 25)$ : a probabilistic approach

Ewain Gwynne, Nina Holden, Joshua Pfeffer +1

There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge ${\mathbf{c}}_{\mathrm M}\in(-\infty,1]…

math.PR2019

External diffusion limited aggregation on a spanning-tree-weighted random planar map

Ewain Gwynne, Joshua Pfeffer

Let $M$ be the infinite spanning-tree-weighted random planar map, which is the local limit of finite random planar maps sampled with probability proportional to the number of spann…

math.PR2018

Connectivity properties of the adjacency graph of SLE $_{κ}$ bubbles for $κ \in (4, 8)$

Ewain Gwynne, Joshua Pfeffer

We study the adjacency graph of bubbles---i.e., complementary connected components---of an SLE $_{κ}$ curve for $κ \in (4, 8)$ , with two such bubbles considered to be adjacent if their…

math.PR2014★ 7 cited

Anchored expansion, speed, and the hyperbolic Poisson Voronoi tessellation

Itai Benjamini, Elliot Paquette, Joshua Pfeffer

We show that random walk on a stationary random graph with positive anchored expansion and exponential volume growth has positive speed. We also show that two families of random tr…

Mathematics of the MML functional quantizer modules for VCV Rack software synthesizer

Wilson loop expectations as sums over surfaces on the plane

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

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

Weak Liouville quantum gravity metrics with matter central charge c∈(−∞,25)

Geodesics and metric ball boundaries in Liouville quantum gravity

Brownian loops and the central charge of a Liouville random surface

KPZ formulas for the Liouville quantum gravity metric

Weak LQG metrics and Liouville first passage percolation

Bounds for distances and geodesic dimension in Liouville first passage percolation

Liouville quantum gravity with matter central charge in (1,25): a probabilistic approach

External diffusion limited aggregation on a spanning-tree-weighted random planar map

Connectivity properties of the adjacency graph of SLEκ​ bubbles for κ∈(4,8)

Anchored expansion, speed, and the hyperbolic Poisson Voronoi tessellation

Weak Liouville quantum gravity metrics with matter central charge $c \in (- \infty, 25)$

Liouville quantum gravity with matter central charge in $(1, 25)$ : a probabilistic approach

Connectivity properties of the adjacency graph of SLE $_{κ}$ bubbles for $κ \in (4, 8)$