13 citations · 111 across the 23 of their papers we have counts for
23 papers
Canonical Local Equilibrium and Cutoff Profiles for the Symmetric Exclusion Process on Discrete Tori
Joe P. Chen
We prove a canonical (or fixed-population) local equilibrium theorem for the symmetric simple exclusion process on the discrete torus , , at particle densitie…
The cutoff profile for exclusion processes in any dimension
Joe P. Chen
Consider symmetric simple exclusion processes, with or without Glauber dynamics on the boundary set, on a sequence of connected unweighted graphs which converge geo…
Cutoffs for exclusion processes on graphs with open boundaries
Joe P. Chen, Milton Jara, Rodrigo Marinho
We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically a…
Cutoffs for exclusion and interchange processes on finite graphs
Joe P. Chen, Rodrigo Marinho
We prove a general theorem on cutoffs for symmetric exclusion and interchange processes on finite graphs , under the assumption that either the graphs converge geome…
Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
Joe P. Chen, Federico Sau
Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then,…
Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly
Joe P. Chen, Ruoyu Guo
The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by un…
Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket
Joe P. Chen, Patrícia Gonçalves
We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the presence of a variable speed boundary.…
Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutions
Joe P. Chen, Jonah Kudler-Flam
We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket () when particles are launched fr…
Local ergodicity in the exclusion process on an infinite weighted graph
Joe P. Chen
We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering…
Internal DLA on Sierpinski gasket graphs
Joe P. Chen, Wilfried Huss, Ecaterina Sava-Huss +1
Internal diffusion-limited aggregation (IDLA) is a stochastic growth model on a graph which describes the formation of a random set of vertices growing from the origin (some fi…
From non-symmetric particle systems to non-linear PDEs on fractals
Joe P. Chen, Michael Hinz, Alexander Teplyaev
We present new results and challenges in obtaining hydrodynamic limits for non-symmetric (weakly asymmetric) particle systems (exclusion processes on pre-fractal graphs) converging…
Regularized Laplacian determinants of self-similar fractals
Joe P. Chen, Alexander Teplyaev, Konstantinos Tsougkas
We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar fractafolds, in the sense of Strichartz. These functions are known to meromorph…
The moving particle lemma for the exclusion process on a weighted graph
Joe P. Chen
We prove a version of the moving particle lemma for the exclusion process on any finite weighted graph, based on the octopus inequality of Caputo, Liggett, and Richthammer. In ligh…
Power dissipation in fractal AC circuits
Joe P. Chen, Luke G. Rogers, Loren Anderson +8
We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have c…
Stabilization by Noise of a -Valued Coupled System
Joe P. Chen, Lance Ford, Derek Kielty +4
Recently Herzog and Mattingly have shown that a -valued polynomial ODE which admits finite-time blow-up solutions may be stabilized by the addition of -valu…
Singularly continuous spectrum of a self-similar Laplacian on the half-line
Joe P. Chen, Alexander Teplyaev
We investigate the spectrum of the self-similar Laplacian, which generates the so-called " random walk" on the integer half-line . Using the method of spectral de…
Fractal AC circuits and propagating waves on fractals
Eric Akkermans, Joe P. Chen, Gerald Dunne +2
We extend Feynman's analysis of the infinite ladder AC circuit to fractal AC circuits. We show that the characteristic impedances can have positive real part even though all the in…
Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials
Ulysses Andrews, Grigory Bonik, Joe P. Chen +2
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation t…
Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
Joe P. Chen, Stanislav Molchanov, Alexander Teplyaev
We establish an asymptotic formulas for the eigenvalue counting function of the Schrödinger operator for some unbounded potentials on several types of unbounded fractal…
Heat kernels on 2d Liouville quantum gravity: a numerical study
Grigory Bonik, Joe P. Chen, Alexander Teplyaev
We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we ver…
Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs
Joe P. Chen, Baris Evren Ugurcan
Consider the free field on a fractal graph based on a high-dimensional Sierpinski carpet (e.g. the Menger sponge), that is, a centered Gaussian field whose covariance is the Green'…
Periodic billiard orbits of self-similar Sierpinski carpets
Joe P. Chen, Robert G. Niemeyer
We identify a collection of periodic billiard orbits in a self-similar Sierpinski carpet billiard table. Based on a refinement of the result of Durand-Cartagena and Tyson regarding…
Statistical mechanics of Bose gas in Sierpinski carpets
Joe P. Chen
We carry out a mathematically rigorous investigation into the equilibrium thermodynamics of massless and massive bosons confined in generalized Sierpinski carpets (GSCs), a class o…