William G. Faris: Publications


  1. Self-Adjoint Operators, Springer, New York, 1975.
  2. Martingale Ideas in Elementary Probability, IUM Mathematics College Publishing House, Moscow, 1996. [pdf]
  3. Diffusion, Quantum Theory, and Radically Elementary Mathematics, edited by W. G. Faris, Princeton University Press, Princeton, NJ, 2006.


  1. "The Trotter product formula for perturbations of semibounded operators," Bull.Amer. Math. Soc. 73 (1967), 211-215. ams.org projecteuclid.org
  2. "The product formula for semigroups defined by Friedrichs extensions," Pacific J. Math. 22 (1967), 47-70. projecteuclid.org
  3. "Product formulas for perturbations of linear propagators," J. Funct. Anal. 1 (1967), 93-108. journals.elsevier.com
  4. "Time decay and the Born series," Rocky Mountain J. Math. 1 (1971), 637-648. projecteuclid.org
  5. "Perturbations and non-normalizable eigenvectors," Helv. Phys. Acta 44 (1971), 930-936. retro.seals.com
  6. "Invariant cones and uniqueness of the ground state for fermion systems," J. Math. Phys. 13 , (1972), 1285-1290. jmp.aip.org
  7. "Quadratic forms and essential self-adjointness," Helv. Phys. Acta 45 (1972), 1074-1088. retro.seals.com
  8. "Essential self-adjointness of operators in ordered Hilbert space," Commun. Math. Phys. 30 (1973), 23-34. projecteuclid.org link.springer.com
  9. "Commutators and self-adjointness of Hamiltonian operators" (with Richard B. Lavine), Commun. Math. Phys. 35 (1974), 39-48. projecteuclid.org
  10. "Degenerate and non-degenerate ground states for Schr "odinger operators" (with Barry Simon), Duke Math. J. 42 (1975), 559-567. projecteuclid.org
  11. "Product spaces and Nelson's inequality," Helv. Phys. Acta 48 (1975), 721-730. retro.seals.com
  12. "Weak Lebesgue spaces and quantum mechanical binding," Duke Math. J. 43 (1976), 365-373. projecteuclid.org
  13. "Inequalities and uncertainty principles," J. Math. Phys. 19 (1978), 461-466. jmp.aip.org
  14. "The stochastic Heisenberg model," J. Funct. Anal. 32 (1979), 342-352. journals.elsevier.com
  15. "The Rayleigh-Schr "odinger expansion of the Gibbs state of a classical Heisenberg ferromagnet," Trans. Amer. Math. Soc. 261 (1980), 579-587. ams.org
  16. "Invariance in calculus," Int. J. Math. Educ. Sci. Technol. 11 (1980), 123-132.
  17. "Spin correlation in stochastic mechanics," Foundations of Physics 12 (1982), 1-26.
  18. "A stochastic picture of spin," in Stochastic Processes in Quantum Theory and Statistical Physics , ed. by S. Albeverio, Ph. Combe, and M. Sirugue-Collin, Springer, Berlin, 1982, 154-168.
  19. "Large fluctuations for a nonlinear heat equation with noise" (with G. Jona-Lasinio), J. Phys. A 15 (1982), 3025-3055.
  20. "Non-linear mechanics of a string in a viscous noisy environment" (with G. Jona-Lasinio), in Structural Elements in Particle Physics and Statistical Mechanics, ed. by J. Honerkamp, K. Pohlmeyer, and H. R "omer, Plenum, New York, 1983, 171-178.
  21. "Localization estimates for a random discrete wave equation at high frequency," J. Stat. Phys. 46 (1987), 477-491. link.springer.com
  22. "A localization principle for multiplicative perturbations," J. Funct. Anal. 67 (1986), 105-114. journals.elsevier.com
  23. "Localization for a random discrete wave equation," in Random Media , IMA Volumes in Mathematics and its Applications, Vol. 7, ed. by G. Papanicolaou, Springer, New York, 1987, 121-127.
  24. "The value of a random game: The advantage of rationality" (with Robert S. Maier), Complex Systems 1 (1987), 235-244.
  25. "Stochastic mechanics," in Encyclopedia of Statistical Sciences Vol. 8, ed. by S. Kotz and N. L. Johnson, Wiley, New York, 1988, 826-830.
  26. "Probabilistic analysis of a learning matrix" (with Robert S. Maier), Advances in Applied Probability 20 (1988), 695-705.
  27. "Scattering of a wave packet by an interval of random medium" (with Woody J. Tsay), J. Math. Phys. 30 (1989), 2900-2903. jmp.aip.org
  28. "Localization estimates for off-diagonal disorder," pp. 391-406 in Mathematics of Random Media , ed. by Werner E. Kohler and Benjamin S. White, Lectures in Applied Mathematics, Vol. 27, American Mathematical Society, Providence, R.I., 1991.
  29. "Order statistics and renormalization," pp 407-416 in Mathematics of Random Media , ed. by Werner E. Kohler and Benjamin S. White, Lectures in Applied Mathematics, Vol. 27, American Mathematical Society, Providence, R.I., 1991.
  30. "Using associated random variables to determine the reliability of neural networks" (with Robert S. Maier), J. Neural Network Computing 2 (1990), 49-52.
  31. "Reliable evaluation of neural networks" (with Robert M. Burton), Neural Networks 4 (1991), 411-415.
  32. "Wave scattering in random media," (with Woody J. Tsay), pp. 51-64 in Probability Models in Mathematical Physics , ed. by G. J. Morrow and W.-S. Yang, World Scientific, Teaneck, New Jersey, 1991.
  33. "Confirmation in experimental mathematics: a case study," (with Robert S. Maier), Complex Systems 5 (1991), 259-264.
  34. "Time delay in random scattering," (with Woody J. Tsay), SIAM J. Appl. Math. 54 (1994), 443-455. siam.org/journals/
  35. "Stability of self-organizing processes," (with Robert M. Burton), in David Aldous and Robin Pemantle, eds., Random Discrete Structures , IMA volumes in Mathematics and its Applications, Volume 76, Springer, New York, 1995, pp. 19-24.
  36. "Random waves and localization," Notices Amer. Math. Soc. 42 (1995), 848-853. ams.org
  37. "Probability in quantum mechanics," appendix to David Wick, The Infamous Boundary: Seven Decades of Controversy in Quantum Physics , Birkh "auser, Boston, 1995.
  38. "A self-organizing cluster process," (with Robert M. Burton), Ann. Appl. Prob. 6 (1996), 1232-1247. projecteuclid.org
  39. "Does quantum probability predict frequency?", Int. J. Quantum Chemistry 65 (1997), 389-398.
  40. "A quantum crystal with multidimensional harmonic oscillators," (with Robert A. Minlos), J. Statistical Physics 94 (1999), 365--387. [pdf] link.springer.com
  41. Letter on ``Consistent Histories and Quantum Measurements'' (Griffiths and Omn\`es article), Physics Today 53 (2000), pp. 15, 72, 74. [pdf]
  42. ``Ornstein-Uhlenbeck and renormalization semigroups,'' Moscow Mathematical J. 1 (2001), 389--405. [pdf]
  43. ``Non-selfadjoint Ornstein-Uhlenbeck semigroups,'' in Fundamental Mathematics Today, edited by S. K. Lando and O. K. Sheinman, Independent University of Moscow and Moscow Center for Continuous Mathematical Education, Moscow, 2003, pp. 294--303. [pdf]
  44. ``A gentle introduction to cluster expansions,'' in Probability and Partial Differential Equations in Modern Applied Mathematics, (IMA Volumes in Mathematics and its Applications 140), edited by Edward C. Waymire and Jinqiao Duan, Springer, New York, 2005, pp. 97--115.
  45. ``Martingales,'' in Encyclopedia of Nonlinear Science, ed. Alwyn Scott, Routledge, New York, 2005, pp. 559--562.
  46. ``Diffusion and where it leads,'' in Diffusion, Quantum Theory, and Radically Elementary Mathematics, edited by W. G. Faris, Princeton University Press, Princeton, NJ, 2006.
  47. ``A connected graph identity and convergence of cluster expansions,'' J. Mathematical Phys. 49, 113302 (2008). jmp.aip.org
  48. ``Combinatorics and cluster expansions,'' Probability Surveys 7 (2010), 157--206. projecteuclid.org
  49. ``Outline of quantum mechanics,'' pp. 1--52 in Entropy and the Quantum, edited by Robert Sims and Daniel Ueltschi, (Contemporary Mathematics 529), American Mathematical Society, Providence, RI, 2010. ams.org ams.org
  50. ``Combinatorial species and cluster expansions,'' Moscow Mathematical J. 10 (2010), 713--727.
  51. ``Combinatorial species and Feynman diagrams,'' S`eminaire Lotharingien de Combinatoire 61A (2011), Article B61An.
  52. ``Biconnected graphs and the multivariate virial expansions,'' Markov Processes Relat. Fields 18 (2012), 357--386.
  53. ``The fundamental theorem of calculus for a matroid,'' J. Math. Phys. 53 , 063305 (2012). jmp.aip.org
  54. ``Rooted tree graphs and the Butcher group: Combinatorics of elementary perturbation theory.'' [pdf]
  55. ``Nelson's early work on probability.'' [pdf]
  56. ``Sliding vectors, line bivectors, and torque.'' [pdf]
  57. ``A groupoid description for plane geometry.'' [pdf]

Book Reviews

  1. review of Methods of Modern Mathematical Physics, vols. III, IV , by M. Reed and B. Simon, in Bull. Math. Soc. 2 (1980), 522-530. ams.org projecteuclid.org
  2. review of Operator Methods in Quantum Mechanics , by M. Schechter, in Bull. Amer. Math. Soc. 6 (1982), 105-109. ams.org projecteuclid.org
  3. review of One-parameter Semigroups , by E. B. Davies, in Acta Applicandae Mathematicae 2 (1984), 391-394.
  4. review of Products of Random Matrices with Applications to Schr "odinger Operators , by P. Bougerol and J. Lacroix, in J. Amer. Stat. Assoc. 83 (1988), 1219-1220.
  5. review of Spectral Theory and Differential Operators , by D. E. Edmunds and W. D. Evans, in Bull. Amer. Math. Soc. 20 (1989), 232-235. ams.org projecteuclid.org
  6. review of Second Year Calculus: From Celestial Mechanics to Special Relativity , by David M. Bressoud, in American Mathematical Monthly 100 (1993), 884-888.
  7. review of Hilbert Space Operators in Quantum Physics , by Jivri Blank, Pavel Exner, and Miloslav Havlivcek, Bull. Amer. Math. Soc. 32 (1995), 339-344. ams.org
  8. review of Shadows of the Mind: A Search for the Missing Science of Consciousness , by Roger Penrose, Notices Amer. Math. Soc. 43 (1996), 203-208. ams.org
  9. review of The Interpretation of Quantum Mechanics , by Roland Omn`es, Notices Amer. Math. Soc. 43 (1996), 1328-1339. ams.org
  10. review of Impostures intellectuelles, by Alan Sokal and Jean Bricmont, Notices Amer. Math. Soc. 45 (1998), 874--876. ams.org
  11. review of The Number Sense: How the Mind Creates Mathematics, by Stanislas Dehaene, Complexity 4 (1998), 46--48.
  12. review of The Collected Works of Eugene Paul Wigner, Part A The Scientific Papers, Vol. 3, edited by Arthur S. Wightman, Studies in History and Philosophy of Modern Physics 30 (1999), 141--143.
  13. review of Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures, by James Robert Brown, Notices Amer. Math. Soc. 47 (2000), 1276--1280. [pdf] ams.org
  14. Featured Review: Quantum Field Theory, review of Quantum Fields and Strings: A Course for Mathematicians, Volumes I and II, edited by Pierre Deligne et al., SIAM Review 43 (2001), 181--195. [pdf]
  15. review of Consistent Quantum Theory, by Robert B. Griffiths, SIAM Review 44 (2002), 726--730. [pdf]
  16. review of It Must Be Beautiful: Great Equations of Modern Science, edited by Graham Farmelo, Notices Amer. Math. Soc. 50 (2003), 361--367. [pdf] ams.org
  17. review of Mathematical Concepts of Quantum Mechanics, by Stephen J. Gustafson and Israel Michael Sigal, SIAM Review 47 (2005), 379--380.
  18. review of Probability Theory: The Logic of Science, by E. T. Jaynes, Notices of the American Mathematical Society 53 (2006), 33--42.ams.org
  19. review of Large Deviations and Metastability, by Enzo Olivieri and Maria Eulalia Vares, SIAM Review 48 (2006), 405--410.
  20. Featured Review: Quantum Field Theory, review of Quantum Field Theory I, by Eberhard Zeidler, SIAM Review 50 (2008), 371--410.
  21. Featured Review: Two books on quantum fields: mathematical guides to a physical theory, review of Quantum Field Theory, by Gerald B. Folland and Quantum Field Theory II, by Eberhard Zeidler, SIAM Review 52 (2010), 381--400.
  22. review of Reflections on Quanta, Symmetries, and Supersymmetries, by V. S. Varadarajan, SIAM Review 54 (2012), 185--190.
  23. review of The Beginning of Infinity, by David Deutsch, Notices Amer. Math. Soc. 59 (2012), 544--552. ams.org
  24. review of Lectures on Quantum Mechanics, by Steven Weinberg, SIAM Review 56 (2014).