2018+ 

13.  Local ergodicity in the exclusion process on an infinite weighted graph (HydroSG Part II). Submitted (2018+) 
In this paper I prove, on every strongly recurrent weighted graph, the coarsegraining arguments needed to pass from the microscopic observables (in the exclusion process) to the corresponding macroscopic averages.
The twoblocks estimate is based on the moving particle lemma established in HydroSG Part I. 

12.  Internal DLA on Sierpinski gasket graphs, with Wilfried Huss, Ecaterina SavaHuss, and Alexander Teplyaev. Submitted (2018+) 
In this paper we prove that starting from a corner vertex of SG, an internal diffusionlimited aggregation process (where successive i.i.d. random walks deposit upon first exit from the previous cluster) fills balls in the graph metric with probability 1. 

11.  From nonsymmetric particle systems to nonlinear PDEs on fractals, with Michael Hinz and Alexander Teplyaev. To appear as Chapter 35 in A. Eberle et al. (Eds.), Stochastic Partial Differential Equations and Related Fields, Springer Proceedings in Mathematics & Statistics (2018). 
This is a summary of a series of four papers (HydroSG Parts I~IV) concerning the hydrodynamic limit of the boundarydriven exclusion process on a resistance space (the Sierpinski gasket being the model space).


10.  Regularized Laplacian determinants of selfsimilar fractals, with Alexander Teplyaev and Konstantinos Tsougkas. Lett. Math. Phys., Online First (2018). 


2017 

9.  The moving particle lemma for the exclusion process on a weighted graph (HydroSG Part I). Electron. Commun. Probab. 22 (2017), paper no. 47. 


8.  Power dissipation in fractal AC circuits, with Luke G. Rogers, Loren Anderson, Ulysses Andrews, Antoni Brzoska, Aubrey Coffey, Hannah Davis, Lee Fisher, Madeline Hansalik, Stephen Loew, and Alexander Teplyaev. (2015 UConn math REU fractals group) J. Phys. A: Math. Theor. 50 325205 (2017) 


7.  Wave equations on onedimensional 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) 9941027. 
(Click here for the wave animations described in the paper.)  
6.  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. (2015 UConn math REU stochastics group) Stoch. Dyn. 17 (2017) 1750046. 
2016 and prior 

5.  Singularly continuous spectrum of a selfsimilar Laplacian on the halfline, with Alexander Teplyaev. J. Math. Phys. 57 052104 (2016). 
4.  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 395203 (2015). 
3.  Entropic repulsion of Gaussian free field on highdimensional Sierpinski carpet graphs, with Baris Evren Ugurcan. Stoch. Proc. Appl. 125 (2015) 46324673. 
2.  Periodic billiard orbits of selfsimilar Sierpinski carpets, with Robert Niemeyer. J. Math. Anal. Appl. 416 (2014) 969994. 
1.  Quantum Theory of CavityAssisted Sideband Cooling of Mechanical Motion, with Florian Marquardt, Aashish Clerk, and Steven M. Girvin. Phys. Rev. Lett. 99 093902 (2007). 
Papers in preparation (2018+) 

P1.  Limit shape universality of cellular automata models on the Sierpinski gasket, with Jonah KudlerFlam. 
P2.  Semilinear evolution equations on resistance spaces (HydroSG Part III), with Michael Hinz and Alexander Teplyaev. 
P3.  Hydrodynamic limit of the boundarydriven exclusion process on the Sierpinski gasket (HydroSG Part IV), with Michael Hinz and Alexander Teplyaev. 
P4.  Anderson localization on infinite fractal lattices, with Stanislav Molchanov and Alexander Teplyaev. 