Stochastic processes, Dirichlet forms, semigroup theory, heat kernels on metric measure spaces, fractals, graphs, limit theorems, random fields, exchangeability.
BV functions and Besov spaces associated with Dirichlet spaces (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev) arXiV.
Analysis on hybrid fractals (with Y. Chen, H. Gu, R.S. Strichartz and Z. Zhou) arXiV.
Canonical diffusions on the pattern spaces of aperiodic Delone sets (with M. Hinz, R. Treviño and A. Teplyaev) arXiV.
Explicit formulas for heat kernels on diamond fractals, to appear in Comm. Math. Phys. (2018) arXiv.
Completely symmetric resistance forms on the stretched Sierpinski gasket (with U. Freiberg and J. Kigami), J. of Fractal Geometry, Nr. 3, Vol. 5: 227-277, 2018. arXiv.
Entropy-based inhomogeneity detection in fiber materials (with E. Spodarev), Methodology and Computing in Applied Probability, 1-17, 2017 (online). arXiv.
Power dissipation in fractal Feynman-Sierpinski AC circuits, Journal of Mathematical Physics, Nr. 7, Vol. 58: 073503, 2017. arXiv.
Estimation of entropy for Poisson marked point processes (with E. Spodarev), Advances in Applied Probability, Nr. 1, Vol.49: 258-278, 2017. arXiv.
Weyl asymptotics for Hanoi atrractors (with U. Freiberg), Forum Mathematicum 29, no. 5, 1003–1022, 2017. arXiv.
The limit theorem for maximum of partial sums of exchangeable random variables (with A. Rakitko), Statistics & Probability Letters, Vol.119: 357-362, 2016. arXiv.
Energy and Laplacian on Hanoi-type fractal quantum graphs (with D. Kelleher and A. Teplyaev), Journal of Physics A: Mathematical and Theoretical, Nr. 4, Vol.49: 1501-1533, 2016. arXiv.
Hanoi attractors and the Sierpinski gasket (with U. Freiberg), Special issue of Int. J. Math. Modelling and Nonlinear Optimization on Fractals, Fractal-based Methods and Applications, Nr. 4, Vol. 3: 251-265, 2012.