My research revolves around Analysis and Probability; in particular I am interested in the interconnections between probabilistic, analytic and geometric aspects of stochastic processes on spaces with a rough structure. Currently I am working on problems related to diffusion processes and heat kernels on metric measure spaces with fractal-like features. I also have some on-going projects that concern the study of (asymptotic) geometric properties of random geometric models featured by random fields.
- Ruiz, P. A., Chen, Y., Gu, H., Strichartz, R. S., & Zhou, Z. (2020). ANALYSIS ON HYBRID FRACTALS. Communications on Pure and Applied Analysis. 19(1), 47-84.
- Ruiz, P. A., Baudoin, F., Chen, L. i., Rogers, L. G., Shanmugalingam, N., & Teplyaev, A. (2020). Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities. JOURNAL OF FUNCTIONAL ANALYSIS. 278(11), 108459-108459.
- Ruiz, P. A., & Spodarev, E. (2018). Entropy-based Inhomogeneity Detection in Fiber Materials. Methodology and Computing in Applied Probability. 20(4), 1223-1239.
- Ruiz, P. A. (2018). Explicit Formulas for Heat Kernels on Diamond Fractals. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 364(3), 1305-1326.
- Alonso-Ruiz, P., & Spodarev, E. (2017). ESTIMATION OF ENTROPY FOR POISSON MARKED POINT PROCESSES. Advances in Applied Probability. 49(1), 258-278.
- NSF - DMS 855349 awarded by National Science Foundation - (Arlington, Virginia, United States) 2019 - 2021
- Feodor Lynen Fellowship awarded by Alexander von Humboldt Foundation - (Bonn, Germany) 2016 - 2018