List of papers on arXiv


Research interests

Stochastic processes, Dirichlet forms, semigroup theory, heat kernels on metric measure spaces, fractals, graphs, limit theorems, random fields, exchangeability.


Preprints

Heat kernel analysis on diamond fractals arXiv.

Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev) arXiV.

Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev) arXiV.

Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev) arXiV.

BV functions and Besov spaces associated with Dirichlet spaces (with F. Baudoin, L. Chen, L. Rogers, N. Shanmugalingam and A. Teplyaev) arXiV.

Canonical diffusions on the pattern spaces of aperiodic Delone sets (with M. Hinz, R. Treviņo and A. Teplyaev) arXiV.


Publications

Analysis on hybrid fractals (with Y. Chen, H. Gu, R.S. Strichartz and Z. Zhou). To appear in Comm. Pure App. Anal. (2019) arXiV.

Explicit formulas for heat kernels on diamond fractals, Comm. Math. Phys. Nr. 3, Vol. 364, 1305-1326 (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.