David P. Herzog

David P. Herzog
Associate Professor
Department of Mathematics
Iowa State University
Office: Carver 474
Email: dherzog at iastate dot edu

Current teaching: Math 554 (see Canvas for further information)
Office hours: TBD (see Canvas for link)

Research Interests: Stochastic ordinary/partial differential equations, PDEs, probability, applied mathematics, control theory.

Short CV

Publications/Preprints:
23) Phase space contraction of degenerately damped random splittings (arXiv), (D.P.Herzog and J.C. Mattingly). Submitted. 43 pages.
22) Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise (arXiv), (F. Baudoin, M. Gordina, D.P. Herzog, J. Kim, T. Melcher). Submitted. 35 pages.
21) Cutoff in the Bernoulli-Laplace model with swaps or order n (journal) (J.S. Alameda, C. Bang, Z. Brennan, D.P. Herzog, J. Kritschgau, E. Sprangel). Electron. Comm. Probab. pp. 1-13 (2024).
20) Stability and invariant measure asymptotics in a model for heavy particles in rough turbulent flows (arXiv) (D.P. Herzog and H.D. Nguyen). Comm. Math. Phys. 405, 49 pages (2024).
19) The method of stochastic characteristics for linear second-order hypoelliptic equations (arXiv) (J. Foldes and D.P. Herzog). Probab. Surveys 20, pp. 113-169 (2023).
18) Gibbsian dynamics and the generalized Langevin equation (arXiv) (D.P. Herzog, J.C. Mattingly, H.D. Nguyen). Electron. J. Probab. 28, pp.1-29 (2023).
17) A functional law of the iterated logarithm for weakly hypoelliptic diffusions at time zero (arXiv) (M. Carfagnini, J. Foldes, D.P. Herzog). Stochastic Process. Appl. 149, pp.188-223 (2022).
16) Weighted L^2-contractivity of Langevin dynamics with singular potentials (arXiv) (E. Camrud, M. Gordina, D.P. Herzog and G. Stoltz). Nonlinearity 35 no. 2, pp.998-1035 (2021).
15) Sensitivity of steady states in a degenerately-damped stochastic Lorenz system (arXiv) (N. Glatt-Holtz, D.P. Herzog, and J. Foldes). Stoch. Dyn. 21 no.8, 32 pages (2021).
14) Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials (arXiv, journal) (F. Baudoin, M. Gordina, and D.P. Herzog). Arch. Ration. Mech. Anal. 241 no. 2 pp.765-804 (2021).
13) The generalized Langevin equation with a power-law memory in a nonlinear potential well (arXiv, journal) (N.E. Glatt-Holtz, D.P. Herzog, S.A. McKinley, and H.D. Nguyen). Nonlinearity 33 no. 6 pp.2820-2852 (2020).
12) Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials (arXiv, journal) (D.P. Herzog and J.C. Mattingly). Comm. Pure Appl. Math. 72 no. 10 pp. 2231-2255 (2019).
11) Exponential relaxation of the Nose-Hoover thermostat under Brownian heating (arXiv, journal) (D.P. Herzog). Commun. Math. Sci. 16 no. 8 pp. 2231-2260 (2018).
10) Scaling and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations (arXiv, journal) (N.E. Glatt-Holtz, D.P. Herzog and J.C. Mattingly). Annals of PDE 4 no. 2 , 103 pages (2018).
9) Geometric ergodicity of two-dimensional Hamiltonian systems with a Lennard-Jones-Like repulsive potential (arXiv, journal) (B. Cooke, D.P. Herzog, J.C. Mattingly, S.A. McKinley, S.C. Schmidler). Commun. Math. Sci. 15 no. 7 pp. 1987-2025 (2017).
8) The small-mass limit for Langevin dynamics with unbounded coefficients and positive friction (arXiv, journal) (D.P. Herzog, S. Hottovy and G. Volpe). J. Stat. Phys. 163 no. 3 pp.659-673 (2016).
7) Noise-induced stabilization of planar flows II (pdf) (D.P. Herzog and J.C. Mattingly). Electron. J. Probab. 20 no. 113 pp.1-37 (2015).
6) Noise-induced stabilization of planar flows I (pdf) (D.P. Herzog and J.C. Mattingly). Electron. J. Probab. 20 no. 111 pp.1-43 (2015).
5) A practical criterion for positivity of transition densities (arXiv, journal)D.P. Herzog and J.C. Mattingly). Nonlinearity 28 pp.2823-2845 (2015).
4) Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies (pdf) (M.D. Ryser, K. McGoff, D.P. Herzog, D.J. Sivakoff and E.R. Myers). Epidemics 11 pp.32-47 (2015).
3) An extension of Hormander's hypoellipticity theorem (arXiv, journal) D.P. Herzog and N. Totz). Potential Anal. 42 pp.403-433 (2015).
2) The transition from ergodic to explosive behavior in a family of stochastic differential equations (arXiv, journal) (J. Birrell, D.P. Herzog, J. Wehr). Stochastic Process. Appl. 122 pp.1519-1539 (2012).
1) Ergodic properties of a model for turbulent dispersion of inertial particles (arXiv, journal) (K. Gawedzki, D.P. Herzog, J. Wehr). Comm. Math. Phys. 308 pp.49-80 (2011).

Ph.D. Dissertation:
Geometry's fundamental role in the stability of stochastic differential equations (pdf) (2011).