Headshot of Professor Mueller.

Carl Mueller

Professor of Mathematics

PhD, University of California, Berkeley

Office Location
802 Hylan Building
Telephone
(585) 441-5029
Web Address
Website

Curriculum Vitae

Biography

I received my PhD from the Berkeley Statistics Department in 1979. I was an NSF postdoc at the University of Illinois from 1979 - 1981, an assistant professor at the University of Texas from 1981 - 1984, and then came to Rochester. Now I’m a full professor. I’ve taken sabbaticals at the University of Minnesota, University of British Columbia, the Math Sciences Research Institute at Berkeley, the Mittag-Leffler Institute outside of Stockholm, and again at the Math Sciences Research Institute at Berkeley.

Research Overview

I am interested in multiparam- eter models driven by noise, often related to models in statistical physics. Currently, my main interest is in stochastic partial differential equations (SPDE). Most physical systems are described in terms of partial differential equations, and random noise influences most of these systems. Thisleads to the study of SPDE. I usually study the qualitative properties of solutions to nonlinear SPDE, such as blow-up, support, die-out, phase transitions, SPDE with singular solutions, and SPDE with vector-valued solutions. I have also dealt with the convergence of particle systems to SPDE. Some of my research is inspired by connections between SPDE and a particle system called the Dawson-Watanabe process (or super-Brownian motion). More re- cently I have studied hitting properties of vector-valued solutions to SPDE, and SPDE and other models which penalize self-intersections.

Research Interests

  • Probability and related parts of analysis

Selected Publications

  • (with D. Khoshnevisan and K. Kim) On the Valleys of the Stochastic Heat Equation, Ann. Appl. Probab. 34, 1B, 1177–1198 (2024)
  • (with D. Khoshnevisan and K. Kim) Dissipation in Parabolic SPDEs II: Oscillation and decay of the solution, Ann.Inst. Henri Poincare, 59, 3, 1610-1641 (2023).
  • (with D. Khoshnevisan, K. Kim, and S-Y Shiu) Phase analysis for a family of stochastic reaction-diffusion equations, Electronic J. Probab., 28, 1-66 (2023).
  • (with E. Neuman) The effective radius of self repelling elastic mani- folds, Ann. Appl. Prob., 33, 6B, 5668-5692 (2023).
  • (with E. Neuman) Scaling properties of a moving polymer, Ann. Appl. Probab. 32, 6, 4251-4278 (2022).
  • (with L. Mytnik and L. Ryzhik) The speed of a random front for stochastic reaction-diffusion equations with strongnoise, Comm. Math. Phys. 384, 699–732 (2021).
  • (with R. Dalang and Y. Xiao) Polarity of almost all points for systems of non-linear stochastic heat equations in the critical dimension, Ann. Probab. 49, 5, 2573-2598 (2021).
  • (with S. Athreya and M. Joseph) Small ball and support theorems for SPDE, Ann. Probab. 49, 5, 2548-2572 (2021).
  • (with R. Dalang, C-Y Lee, and Y. Xiao) Multiple points of Gaussian random fields, Electronic J. Probab., 26, paperno. 17, 1-25 (2021).
  • (with D. Khoshnevisan, K. Kim, and S-Y Shiu) Dissipation in parabolic SPDEs, J. Stat. Phys. 179, 2, 502-534 (2020).
  • (with L. Mytnik and J. Quastel) Effect of noise on front propagation in reaction-diffusion equations of KPP type, Invent. Math. 184, 2, 405-453 (2011).