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Professor Alexander Belton CMath, CSci, FIMA, SFHEA

Head of Department, Professor of Mathematics

  1. 2020
  2. Forthcoming

    A panorama of positivity. II: fixed dimension

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 30/03/2020, (Accepted/In press) Complex Analysis and Spectral Theory. Dales, H. G., Khavinson, D. & Mashreghi, J. (eds.). Providence, RI: American Mathematical Society, p. 109-150 42 p. (Contemporary Mathematics; vol. 743).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)

  3. 2019
  4. Published

    Simultaneous kernels of matrix Hadamard powers

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 1/09/2019, In : Linear Algebra and its Applications. 576, p. 142-157 16 p.

    Research output: Contribution to journalJournal article

  5. Published

    Quasifree Stochastic Cocycles and Quantum Random Walks

    Belton, A. C. R., Gnacik, M., Lindsay, J. M. & Zhong, P., 15/07/2019, In : Journal of Statistical Physics. 176, 1, p. 1-39 39 p.

    Research output: Contribution to journalJournal article

  6. Published

    A panorama of positivity. I: dimension free

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 31/05/2019, Analysis of Operators on Function Spaces: The Serguei Shimorin Memorial Volume. Aleman, A., Hedenmalm, H., Khavinson, D. & Putinar, M. (eds.). Cham: Birkhauser, p. 117-165 49 p. (Trends in Mathematics).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter (peer-reviewed)

  7. Published

    On stopping Fock-space processes

    Belton, A. C. R., 03/2019, In : Journal of Theoretical Probability. 32, 1, p. 484-526 43 p.

    Research output: Contribution to journalJournal article

  8. Published

    Introduction to classical and quantum Markov semigroups

    Belton, A., 2019, Open Quantum Systems: A Mathematical Perspective. Bahns, D., Pohl, A. & Witt, I. (eds.). Cham: Birkhauser, p. 1-54 54 p. (Tutorials, Schools, and Workshops in the Mathematical Sciences).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

  9. 2018
  10. Published

    Strong convergence of quantum random walks via semigroup decomposition

    Belton, A. C. R., Gnacik, M. & Lindsay, J. M., 06/2018, In : Annales Henri Poincaré. 19, 6, p. 1711-1746 36 p.

    Research output: Contribution to journalJournal article

  11. 2017
  12. Published

    The cocycle identity holds under stopping

    Belton, A. C. R. & Sinha, K. B., 1/09/2017, In : The Quarterly Journal of Mathematics. 68, 3, p. 817-830 14 p.

    Research output: Contribution to journalJournal article

  13. 2016
  14. Published

    Moment-sequence transforms

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 27/10/2016, Arxiv, 33 p.

    Research output: Working paper

  15. Published

    Matrix positivity preservers in fixed dimension. I

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 6/08/2016, In : Advances in Mathematics. 298, p. 325-368 44 p.

    Research output: Contribution to journalJournal article

  16. Published

    Schur polynomials and matrix positivity preservers

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 25/05/2016, Proceedings of the 28th International Conference on Formal Power Series and Algebraic Combinatorics: FPSAC 2016 Vancouver, Canada. DMTCS Proceedings, p. 155-166 12 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNConference contribution/Paper

  17. Published

    Matrix positivity preservers in fixed dimension

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 02/2016, In : Comptes Rendus Mathématique. 354, 2, p. 143-148 6 p.

    Research output: Contribution to journalJournal article

  18. 2015
  19. Published

    An algebraic construction of quantum flows with unbounded generators

    Belton, A. C. R. & Wills, S. J., 2015, In : Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 51, 1, p. 349-375 27 p.

    Research output: Contribution to journalJournal article

  20. 2014
  21. Published
  22. Published

    Quantum Feynman-Kac perturbations

    Belton, A. C. R., Lindsay, J. M. & Skalski, A. G., 02/2014, In : Journal of the London Mathematical Society. 89, 1, p. 275-300 26 p.

    Research output: Contribution to journalJournal article

  23. Published

    Quantum random walks with general particle states

    Belton, A. C. R., 2014, In : Communications in Mathematical Physics. 328, 2, p. 573-596 24 p.

    Research output: Contribution to journalJournal article

  24. Published

    Stopping the CCR flow and its isometric cocycles

    Belton, A. C. R. & Sinha, K. B., 2014, In : The Quarterly Journal of Mathematics. 65, 4, p. 1145-1164 20 p.

    Research output: Contribution to journalJournal article

  25. 2013
  26. Published

    On stopping Fock-space processes

    Belton, A. C. R., 20/11/2013, 40 p.

    Research output: Working paper

  27. 2012
  28. Published

    A vacuum-adapted approach to quantum Feynman-Kac formulae

    Belton, A. C. R., Lindsay, J. M. & Skalski, A., 03/2012, In : Communications on Stochastic Analysis. 6, 1, p. 95-109 15 p.

    Research output: Contribution to journalJournal article

  29. 2010
  30. Published

    Quantum random walks and thermalisation

    Belton, A. C. R., 12/2010, In : Communications in Mathematical Physics. 300, 2, p. 317-329 13 p.

    Research output: Contribution to journalJournal article

  31. Published

    Random-walk approximation to vacuum cocycles

    Belton, A. C. R., 04/2010, In : Journal of the London Mathematical Society. 81, 2, p. 412-434 23 p.

    Research output: Contribution to journalJournal article

  32. 2008
  33. Published

    Approximation via toy Fock space - the vacuum-adapted viewpoint

    Belton, A. C. R., 09/2008, Quantum Stochastics and Information. Belavkin, V. P. & Guţă, M. (eds.). Singapore: World Scientific, p. 3-22 20 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

  34. Published

    On the path structure of a semimartingale arising from monotone probability theory

    Belton, A. C. R., 2008, In : Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 44, 2, p. 258-279 22 p.

    Research output: Contribution to journalJournal article

  35. 2007
  36. Published

    The chaotic-representation property for a class of normal martingales

    Belton, A. C. R. & Attal, S., 1/11/2007, In : Probability Theory and Related Fields. 139, 3-4, p. 543-562 20 p.

    Research output: Contribution to journalJournal article

  37. Published

    Alicki-Fannes and Hudson-Parthasarathy evolution equations

    Belton, A. C. R., 07/2007, Quantum Probability and Infinite Dimensional Analysis XX. Accardi, L., Freudenberg, W. & Schuermann, M. (eds.). Singapore: World Scientific, p. 128-133 6 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

  38. 2006
  39. Published

    Some self-adjoint quantum semimartingales

    Belton, A. C. R., 1/05/2006, In : Proceedings of the London Mathematical Society. 92, 3, p. 791-816 26 p.

    Research output: Contribution to journalJournal article

  40. Published

    The monotone Poisson process

    Belton, A. C. R., 2006, Quantum Probability. Bożejko, M., Młotkowski, W. & Wysoczański, J. (eds.). 73 ed. Warsaw: Polish Academy of Sciences, p. 99-115 17 p. (Banach Center Publications).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

  41. 2005
  42. Published

    A note on vacuum-adapted semimartingales and monotone independence

    Belton, A. C. R., 01/2005, Quantum Probability and Infinite Dimensional Analysis XVIII. Schuermann, M. & Franz, U. (eds.). Singapore: World Scientific, p. 105-114 10 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

  43. 2004
  44. Published

    Erratum: An isomorphism of quantum semimartingale algebras (Quarterly Journal Mathematics (2004) 55 (135-165) DOI: 10.1093/qmath/hag052)

    Belton, A. C. R., 1/12/2004, In : Quarterly Journal of Mathematics. 55, 4, 1 p.

    Research output: Contribution to journalComment/debate

  45. Published

    An isomorphism of quantum semimartingale algebras

    Belton, A. C. R., 06/2004, In : The Quarterly Journal of Mathematics. 55, 2, p. 135-165 31 p.

    Research output: Contribution to journalJournal article

  46. 2001
  47. Published

    Quantum Ω-semimartingales and stochastic evolutions

    Belton, A. C. R., 1/12/2001, In : Journal of Functional Analysis. 187, 1, p. 94-109 16 p.

    Research output: Contribution to journalJournal article

  48. 1998
  49. Unpublished

    A matrix formulation of quantum stochastic calculus

    Belton, A. C. R., 1998, (Unpublished) University of Oxford. 110 p.

    Research output: ThesisDoctoral Thesis

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