Jean-Claude Zambrini

Retired associate professor at the Department of Mathematics of the Faculty of Sciences of the University of Lisbon.

Former director of the Grupo de Física Matemática, from 2002 to January 2024.

Principal investigator in the project “Schroedinger’s problem and Optimal Transport: a multidisciplinary perspective” (PTDC/MAT-STA/28812/2017), financed by the FCT.

Research interests

• Probabilistic methods in mathematical physics.
• Path integral methods in quantum theory (and quantum field theory).
• Classical and quantum dynamical systems (geometric and algebraic methods). Stochastic deformation.
• Applications of stochastic analysis.

Selected publications

• With Q. Huang:
  From second order differential geometry to stochastic geometric mechanics, J. Nonlinear Sci. 33 (2023), 6, 127 pp.

• With Q. Huang:
  “Stochastic geometric mechanics in nonequilibrium thermodynamics: Schrödinger meets Onsager”, J. Phys A 56 (2023), 134003, 24 pp.

• With A.B. Cruzeiro and C. Oliveira:
  “Time-symmetric optimal stochastic control problems in space-time domains”, Optimization 71 (2022), 3241-3275.

• With M. Arnaudon, A. B. Cruzeiro and C. Léonard:
  “An entropic interpolation problem for incompressible viscous fluids” Annales de l’Institut Henri Poincaré – Probabilités et Statistiques 56, 3 (2020), 2211-2235. URL: http://gfm.cii.fc.ul.pt/people/jczambrini/AIHP1036.pdf
• With M. Arnaudon:
  “A Stochastic Look at Geodesics on the Sphere” in Geometric Science of
  Information”, Springer International Publishing (2017).
• With R. Lassalle:
  “A weak approach to the stochastic deformation of classical mechanics”, J. Geom. Mech. 8, 2 (2016), 221-233.
• With P. Vuillermot:
  “On some Gaussian Bernstein processes in R^N and the periodic Ornstein–Uhlenbeck process”, Stoch. Anal. Appl. 34, 4 (2016), 573-597.
• With N. Privault and X. Yang:
  “Large deviations for Bernstein bridges”, Stoch. Process. Appl.
  126, 5 (2016), 1285-1305.
• With C. Léonard and S. Roelly:
  “Reciprocal processes. A measure-theoretical point of view”, Probab.
  Surv. 11 (2014), 237-269.
• “Stochastic Deformation of Classical Mechanics”, Discrete and Continuous Dynamical Systems, 2013 supplement (2013), 807-813.
• “The research program of Stochastic Deformation (with a view toward Geometric Mechanics)”
  Progress in Probability 68, Springer (2015), 359-393.
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/JCZambrini_EPFL.pdf
• With Pierre A. Vuillermot:
  “Bernstein Diffusions for a Class of Linear Parabolic Partial
  Differential Equations”, Journal of Theoretical Probability (May 2012).
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/vuizambrini1.pdf
• With N. Privault:
  “Stochastic deformation of integrable dynamical systems and random time
  symmetry”,
  URL: http://www.ntu.edu.sg/home/nprivault/papers/deformation.pdf
• “On the geometry of the Hamilton-Jacobi-Bellman equation”, Journal of Geometric Mechanics 1, 3 (Sep 2009).
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/geometry-hamilton-jacobi-bellman.pdf
• With Wu Liming and A. B. Cruzeiro:
  “Bernstein processes associated with a Markov process”, in Stochastic Analysis and Mathematical Physics, ANESTOC’98, Proceedings of the Third
  International Workshop, Ed. R. Rebolledo, Trends in Mathematics Series, Birkhäuser, Boston (2000).
  URL: http://www.birkhauser.ch/books/math/4185.htm
• With Kai Lai Chung:
  Introduction to Random Time and Quantum Randomness, New Edition, Monographs of the Portuguese Mathematical Society vol. 1, World Scientific (2003).
  URL: http://www.worldscibooks.com/physics/5288.html
• With N. Privault:
  “Markovian bridges and reversible diffusion processes with jumps”, Annales de l’Institut Henri Poincaré (Probabilités & Statistiques) 40 (2004), 599-633.
  URL: http://www.ntu.edu.sg/home/nprivault/papers/bridges.pdf
• With P. Lescot:
  “Probabilistic deformation of contact geometry, diffusion processes and their quadratures”, Progress in Probability 59, Birkhauser Verlag Basel (2007), 203-226.
  URL:
  http://gfm.cii.fc.ul.pt/people/jczambrini/lescot-zambrini-ascona.pdf
• With N. Privault:
  “Euclidean quantum mechanics in the momentum representation”,
  Journal of Mathematical Physics 46 (2005).
  URL: http://www.ntu.edu.sg/home/nprivault/papers/euclidean.pdf
• Editor, with Rolando Rebolledo and Jorge Rezende:
  Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC 2002), Proceedings of the Mathematical Legacy of R P Feynman (Lisbon, Portugal, 3-7 June 2002), Proceedings of the Open Systems and Quantum Statistical Mechanics (Santiago, Chile, 7-11 January 2002), World Scientific (2004).
  URL: http://www.worldscibooks.com/physics/5676.html
• Editor:
  XIVth International Congress on Mathematical Physics (Lisbon, Portugal 28 July – 2 August 2003), World Scientific (2006).
  URL: http://www.worldscibooks.com/physics/5778.html
• Editor, with J. C. Mourão, J. P. Nunes, R. Picken:
  Prospects in Mathematical Physics (YRS of 14th ICMP 2003), Contemporary Mathematics no 437, American Mathematical Society (2007).
  URL: http://www.ams.org/bookstore?fn=20&item=CONM-437
• With S. Albeverio and J. Rezende:
  “Probability and quantum symmetries II.The theorem of Noether in
  quantum mechanics”, Journal of Mathematical Physics 47 (2006).
  URL: http://gfm.cii.fc.ul.pt/people/jczambrini/JMathPhys-47-062107.pdf
• Editor, with Gerard Ben Arous, Ana Bela Cruzeiro, Yves Le Jan:
  Stochastic Analysis in Mathematical Physics, Proceedings of a Satellite Conference of ICM 2006 (Lisbon, Portugal 4-8 September 2006), World
  Scientific (2008).
  URL http://www.worldscibooks.com/mathematics/6734.html