(The papers below have been either published, accepted, or conditionally accepted for publication. See my ARXIV PAGE for the most up-to-date list of my papers.)
2021
Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket.
(with Patrícia Gonçalves.) Math. Phys. Anal. Geom. 24, article no. 24 (2021). ARXIV:1904.08789
Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems.
(with Federico Sau.) Markov Processes Relat. Fields 27, 339-380 (2021). ARXIV:2008.13403
2020
Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly.
(with Ruoyu Guo '19.) Commun. Math. Phys. 380, 187-243 (2020). ARXIV:1909.05662
Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutions.
(with Jonah Kudler-Flam '17.) Ann. Inst. Henri Poincaré Comb. Phys. Interact. 7 (2020), 585-664. ARXIV:1807.08748
Internal DLA on Sierpinski gasket graphs.
(with Wilfried Huss, Ecaterina Sava-Huss, and Alexander Teplyaev.) Chapter 7 in "Analysis and Geometry on Graphs & Manifolds," M. Keller et al. (Eds.), London Mathematical Society Lecture Notes, Cambridge University Press (2020). ARXIV:1702.04017
Fractal AC circuits and propagating waves on fractals.
(with Eric Akkermans, Gerald Dunne, Luke G. Rogers, and Alexander Teplyaev.) Chapter 18 in "Analysis, Probability, and Mathematical Physics on Fractals," P. Alonso-Ruiz et al. (Eds.), World Scientific Publishing (2020). ARXIV:1507.05682
Analysis, Probability and Mathematical Physics on Fractals. Patricia Alonso-Ruiz, Joe P. Chen, Luke G. Rogers, Robert S. Strichartz, and Alexander Teplyaev (Eds.). World Scientific Publishing (2020).
2018
From non-symmetric particle systems to non-linear PDEs on fractals.
(with Michael Hinz and Alexander Teplyaev.) To appear in the proceedings for Stochastic PDEs and Related Fields: an international conference in honor of Michael Röckner's 60th birthday. (2018). ARXIV:1702.03376
Regularized Laplacian determinants of self-similar fractals.
(with Alexander Teplyaev and Konstantinos Tsougkas.) Lett. Math. Phys. 108 (2018) 1563-1579. ARXIV:1610.10062
2017
The moving particle lemma for the exclusion process on a weighted graph.
Electron. Commun. Probab. 22 (2017), paper no. 47. ARXIV:1606.01577
Power dissipation in fractal AC circuits.
(with Luke G. Rogers, Loren Anderson, Ulysses Andrews, Antoni Brzoska, Aubrey Coffey, Hannah Davis, Lee Fisher, Madeline Hansalik, Stephew Loew, and Alexander Teplyaev.). J. Phys. A: Math. Theor. 50 (2017) 325205. ARXIV:1605.03890
Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials.
(with Ulysses Andrews, Grigory Bonik, Richard W. Martin, and Alexander Teplyaev.)
J. Fourier Anal. Appl. 23 (2017) 994--1027. ARXIV:1505.05855
Stabilization by noise of a $\mathbb{C}^2$-valued coupled system.
(with Lance Ford, Derek Kielty, Rajeshwari Majumdar, Heather McCain, Dylan O'Connell, and Fan Ny Shum.) Stoch. Dyn. 17 (2017) 1750046. ARXIV:1510.09221
2016 and prior
Singularly continuous spectrum of a self-similar Laplacian on the half-line.
(with Alexander Teplyaev.) J. Math. Phys. 57 (2016) 052104. ARXIV:1509.08875
Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces.
(with Stanislav Molchanov and Alexander Teplyaev.) J. Phys. A: Math. Theor. 48 (2015) 395203. ARXIV:1505.03923
Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs.
(with Baris E. Ugurcan.) Stoch. Proc. Appl. 125 (2015) 4632--4673. ARXIV:1307.5825
Periodic billiard orbits of self-similar Sierpinski carpets.
(with Robert G. Niemeyer.) J. Math. Anal. Appl. 416 (2014) 969--994. ARXIV:1303.4032
Quantum theory of cavity-assisted sideband cooling of mechanical motion.
(with Florian Marquardt, Aashish A. Clerk, and Steven M. Girvin.)
Phys. Rev. Lett. 99, 093902 (2007).
