Fine Hall, Room 207
Princeton University
Princeton, NJ 08544
(609) 258 0973
E-mail: rvan AT math.princeton.edu
My interests lie broadly in probability theory, analysis, geometry,
and their interactions. I am particularly fascinated by the development of
principles and methods that explain the common structure in a variety of
pure and applied mathematical problems. My recent focus has been on
high-dimensional phenomena in probability and on convex geometry; I also
have a long-standing interest in conditional phenomena in probability and
ergodic theory, and in noncommutative probability.
Matrix chaos inequalities and chaos of combinatorial type (with Afonso Bandeira, Kevin Lucca, Petar Nizić-Nikolac).
Preprint. [PDF][arXiv]
A new approach to strong convergence II. The classical ensembles (with Chi-Fang Chen and Jorge Garza-Vargas).
Preprint. [PDF][arXiv]
A new approach to strong convergence (with Chi-Fang Chen, Jorge Garza-Vargas, Joel Tropp).
Preprint. [PDF][arXiv]
Matrix concentration inequalities and free probability II. Two-sided bounds and applications (with Afonso Bandeira, Giorgio Cipolloni, Dominik Schröder).
Preprint. [PDF][arXiv]
Extremal random matrices with independent entries and matrix superconcentration inequalities (with Tatiana Brailovskaya).
Preprint. [PDF][arXiv]
The extremals of the Kahn-Saks inequality (with Alan Yan and Xinmeng Zeng).
Adv. Math. 456, 109892 (2024). [Journal][arXiv]
A localization-delocalization transition for nonhomogeneous random matrices (with Laura Shou).
J. Stat. Phys. 191, 26 (2024). [Journal][arXiv]
Matrix concentration inequalities and free probability (with Afonso Bandeira and March Boedihardjo).
Invent. Math. 234, 419-487 (2023). [Journal][arXiv]
The local logarithmic Brunn-Minkowski inequality for zonoids
Geom. Aspects of Funct. Anal., Lecture Notes in Mathematics 2327, Springer, pp. 355-379 (2023). [Journal][arXiv]
Shephard's inequalities, Hodge-Riemann relations, and a conjecture of Fedotov
Geom. Aspects of Funct. Anal., Lecture Notes in Mathematics 2327, Springer, pp. 337-354 (2023). [Journal][arXiv]
The extremals of the Alexandrov-Fenchel inequality for convex polytopes (with Yair Shenfeld)
Acta Math. 231, 89-204 (2023). [Journal][arXiv]
Expository survey: Proceedings of ICBS 2024 (Frontiers of Science Award). [PDF]
The extremals of Minkowski's quadratic inequality (with Yair Shenfeld).
Duke Math. J. 171, 957-1027 (2022). [Journal][arXiv]
A theory of universal learning (with S. Hanneke, S. Moran, A. Yehuydayoff, O. Bousquet)
STOC 2021 (conference version) 53, 532–541 (2021). [PDF][arXiv]
Rademacher type and Enflo type coincide (with Paata Ivanisvili and Alexander Volberg)
Ann. of Math. 192, 665-678 (2020). [Journal][arXiv]
Mixed volumes and the Bochner method (with Yair Shenfeld)
Proc. Amer. Math. Soc. 147, 5385-5402 (2019). [Journal][arXiv]
Second-order converses via reverse hypercontractivity (with Jingbo Liu and Sergio Verdu)
Math. Stat. Learn. 2, 103-163 (2019). [Journal][arXiv]
Conference version:
Proc. ISIT 2017 (Aachen), 943--947 (2017). [Journal][PDF]
The dimension-free structure of nonhomogeneous random matrices (with Rafał Latała and Pierre Youssef)
Invent. Math. 214, 1031-1080 (2018). [Journal][arXiv]
Expository note (in French): CNRS Actualité Scientifique, May 2019. [PDF]
The equality cases of the Ehrhard-Borell inequality (with Yair Shenfeld)
Adv. Math. 331, 339-386 (2018). [Journal][arXiv]
Chaining, interpolation, and convexity II: The contraction principle
Ann. Probab. 46, 1764-1805 (2018). [Journal][arXiv]
Chaining, interpolation, and convexity
J. Eur. Math. Soc. 20, 2413-2435 (2018). [Journal][arXiv]
The Borell-Ehrhard game
Probab. Th. Rel. Fields 170, 555-585 (2018). [Journal][arXiv]
On the spectral norm of Gaussian random matrices
Trans. Amer. Math. Soc. 369, 8161-8178 (2017). [Journal][arXiv]
Sharp nonasymptotic bounds on the norm of random matrices with independent entries (with Afonso Bandeira)
Ann. Probab. 44, 2479-2506 (2016). [Journal][arXiv]
Consistent order estimation and minimal penalties (with Elisabeth Gassiat)
IEEE Trans. Inform. Theory 59, 1115-1128 (2013). [Journal][arXiv]
On the exchange of intersection and supremum of σ-fields in filtering theory
Israel J. Math. 192, 763-784 (2012). [Journal][arXiv]
Ergodicity and stability of the conditional distributions of nondegenerate Markov chains (with X. Thomson Tong)
Ann. Appl. Probab. 22, 1495-1540 (2012). [Journal][arXiv]
On the minimal penalty for Markov order estimation
Probab. Th. Rel. Fields 150, 709-738 (2011). [Journal][arXiv]
Consistency of the maximum likelihood estimator for general hidden Markov models (with Randal Douc, Eric Moulines, Jimmy Olsson)
Ann. Statist. 39, 474-513 (2011). [Journal][arXiv]
Intrinsic methods in filter stability (with Pavel Chigansky, R. Liptser)
In Oxford Handbook of Nonlinear Filtering (D. Crisan and B. Rozovsky, eds.), Oxford University Press, 2011. [PDF]
A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains (with Pavel Chigansky)
Ann. Appl. Probab. 20, 2318-2345 (2010). [Journal][arXiv]
Nonlinear filtering and systems theory
Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010 semi-plenary paper). [PDF]
When do nonlinear filters achieve maximal accuracy?
SIAM J. Control Optim. 48, 3151-3168 (2009). [Journal][arXiv]
Uniform time average consistency of Monte Carlo particle filters
Stoch. Proc. Appl. 119, 3835-3861 (2009). [Journal][arXiv]
The stability of conditional Markov processes and Markov chains in random environments
Ann. Probab. 37, 1876-1925 (2009). [Journal][arXiv]
Uniform observability of hidden Markov models and filter stability for unstable signals
Ann. Appl. Probab. 19, 1172-1199 (2009). [Journal][arXiv]
Discrete time nonlinear filters with informative observations are stable
Electr. Commun. Probab. 13, 562-575 (2008). [Journal][arXiv]
Filtering, Stability, and Robustness
Ph.D. Thesis, California Institute of Technology (2007). [PDF]
Model robustness of finite state nonlinear filtering over the infinite time horizon (with Pavel Chigansky)
Ann. Appl. Probab. 17, 688-715 (2007). [Journal][arXiv]
Almost global stochastic stability
SIAM J. Control Optim. 45, 1297-1313 (2006). [Journal][arXiv]
Older work (in physics)
The stability of quantum Markov filters
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, 153-172 (2009). [PDF][arXiv]
A discrete invitation to quantum filtering and feedback control (with Luc Bouten, Matt James)
SIAM Review 51, 239-316 (2009). [Journal][arXiv]
Discrete approximation of quantum stochastic models (with Luc Bouten)
J. Math. Phys. 49, 102109 (2008). [Journal][arXiv]
Approximation and limit theorems for quantum stochastic models with unbounded coefficients (with Luc Bouten, Andrew Silberfarb)
J. Funct. Anal. 254, 3123-3147 (2008). [Journal][arXiv]
On the separation principle of quantum control (with Luc Bouten)
In Quantum Stochastics and Information: Statistics, Filtering and Control (V. P. Belavkin and M. I. Guta, eds.), World Scientific, 2008. [arXiv]
An introduction to quantum filtering (with Luc Bouten, Matt James)
SIAM J. Control Optim. 46, 2199-2241 (2007). [Journal][arXiv]
Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode (with John Gough)
J. Stat. Phys. 127, 575-607 (2007). [Journal][arXiv]
Stabilizing feedback controls for quantum systems (with Mazyar Mirrahimi)
SIAM J. Control Optim. 46, 445-467 (2007). [Journal][arXiv]
Feedback Control of Quantum State Reduction (with John K. Stockton, Hideo Mabuchi)
IEEE Trans. Automat. Control 50, 768-780 (2005). [Journal][arXiv]
Modelling and feedback control design for quantum state preparation (with John K. Stockton, Hideo Mabuchi)
J. Opt. B: Quantum Semiclass. Opt. 7, S179-S197 (2005). [Journal]
Quantum projection filter for a highly nonlinear model in cavity QED (with Hideo Mabuchi)
J. Opt. B: Quantum Semiclass. Opt. 7, S226-S236 (2005). [Journal][arXiv]
Single-Particle Self-Excited Oscillator (with Brian D'Urso, Brian Odom, D. Hanneke, G. Gabrielse)
Phys. Rev. Lett. 94, 113002 (2005). [Journal][PDF]
Deterministic Dicke-state preparation with continuous measurement and control (with John K. Stockton, Hideo Mabuchi)
Phys. Rev. A 70, 022106 (2004). [Journal][arXiv]