I am currently a Zuckerman Postdoctoral Scholar at The Technion הטכניון, Israel, hosted by Leonid Mytnik and Haya Kaspi.
My current research involves estimating the speed of wave-fronts for KPP-equations with noise. In general, my research area is probability theory motivated by statistical physics.
I have worked across disciplines as a statistical consultant while in the MS Statistics program at UW.
Past (and some current work) of mine involves large scale behavior of interacting diffusions motivated by statistical physics and statistical thermodynamics. In these problems we determine the PDE/free boundary problem resulting as the limit of the empirical processes as the number of particles become large. Typically we also show existence and uniqueness of the PDE.
I received my PhD under Krzysztof Burdzy at the University of Washington, Seattle.
I previously co-organized (w Tobias Hurth) the ANR-MALIN conference June 10-14, 2019, which took place in the mountainous Les Diablerets, Switzerland. The next conference will take place in CIRM, Marseille. (Postdocs/grad students associated with ANR or MALIN are especially encouraged).
The image adjacent to the photo was generated by a group of undergraduates I worked with in the Washington eXperimental Math Lab (WXML). They used computational methods to confirm conjectures for the Hausdorff dimension of the Brownian earthworm model. They compared two computational methods to estimate the Hausdorff dimension of fractals. Check out this list of fractals and their Hausdorff dimension.
Talks: (Invited) Berlin (April 9th, 2020), Northeast Probability Seminar, CUNY (November 21, 2019); Oxford (June 17, 2019); EPFL, Lausanne; SMSA (TU Dresden); University of Zagreb, Croatia; XXI Escola Brasileira de Probabilidade IMPA, Rio de Janeiro.
- Forthcoming/Current Projects:
- Existence and uniqueness of KPP equation with Hölder drift. (With Leonid Mytnik and Zhenyao Sun.)
- A Thermal to Kinetic Energy Exchanging Insulator. With Zhen-Yao Sun.
- Speed-front of wave-front for Stochastic KPP equation with Hölder Drift. with Zhen-Yao Sun and Leonid Mytnik.
- Large scale behavior of systems of reflecting diffusions with local-time dependent drift. with Haya Kaspi. (Pre-arXiv, early version)
- Convergence of jump processes with stochastic intensity to Brownian motion with inert drift. Bernoulli.
- Propagation of chaos for reflecting diffusions with local time dependent noise. (Submitted). 2020.
- Hydrodynamic limit and Propagation of Chaos for Brownian Particles reflecting from a Newtonian barrier. Annal. Appl. Probab. 2019.
- Billiards with Markovian reflection laws, with Krzysztof Burdzy and Carl-Erik Gauthier. Electron. J. Probab. 2019.
- Stable Systems of Competing L\'evy Particles, with Andrey Sarantsev. Brazilian J. Probab. (2019).
- (Statistical Consultant) Residential Building Lifespan and Community Turnover. Alex Ianchenko; Kathrina Simonen; Clayton Barnes. Journal of Architectural Engineering.
Contact: clayleroy2[at]gmail.com; cbarnes[at]campus.technion.ac.il