Quantum operators in classical probability theory: I. "Quantum spin" techniques and the exclusion model of diffusion

Stochastic Processes and their Applications

Volumn 61, Issue 2, 1996, Pages 205-221

  Lloyd, Peter ^a   Sudbury, Aidan ^a   Donnelly, Peter ^b  

^a MONASH UNIVERSITY   (Australia)

^b NONE

Author keywords

Exclusion process; Quantum spin

Indexed keywords

EID: 0030078059     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-4149(96)84552-2     Document Type: Article

References (14)

1. R. Brout, Phase Transitions (Benjamin, 1965).
2. R. Brout, Phase transitions, in: M. Chretien, E.P. Gross and S. Deser, eds., Statistical Physics, Phase Transitions and Superfluidity. Vol. I (1968) (Gordon and Beach, London).
3. E.T. Copson, Asymptotic Expansions (Cambridge Univ. Press, Cambridge, England, 1965).
4. B. Derrida, M.R. Evans, V. Hakim and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation. J. Phys. A: Math. Gen. 26 (1993) 1493-1517.
5. L. Devroye and A Sbihi, Random walks on highly symmetric graphs, J. Theory Probab. 3 (1990) 497-514.
6. P. Diaconis, R. Graham and J. Morrison, Asymptotic analysis of a random walk on a hypercube with many dimensions, in: Random Structures and Algorithms, Vol. I (1990) pp. 57-72.
7. P. Diaconis and M. Shahshahani, Time to reach stationarity in the Bernoulli-Laplace diffusion model. SIAM J. Math. Anal. 18 (1987) 208-218.
8. P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford Univ. Press, London, 1958).
9. P. Donnelly, P. Lloyd and A. Sudbury, Approach to stationarity of the Bernoulli-Laplace diffusion model. Adv. Appl. Probab. 26 (1994) 715-727.
10. P.C. Hemmer and J.L Lebowitz, Systems with weak long-range interactions, in: C. Domb and M.S. Green, eds., Phase Transitions and Critical Phenomena, Vol. 5B, Academic Press, London, 1976.
11. A. Huber, Variational principles in quantum statistical mechanics, in: R.C. Clark and G.H. Derrick, eds., Mathematical Methods in Solid State and Superfluid Theory (Plenum Press, New York, 1968).
12. A.M. Khorunzhy, B.A. Khoruzhenko, L.A. Pastur and M.V. Shcherbina, in: Phase Transitions and Critical Phenomena, ed., C. Domb and J.L. Lebowitz. 15, 73-239 (Academic Press, New York, 1992).
13. T. Liggett, Interacting Particle Systems (Springer, New York, 1985).
14. G.S. Rushbrooke, G.A. Baker and P.J. Wood, The Heisenberg model, in: C. Domb and M.S. Green, eds., Phase Transitions and Critical Phenomena, Vol. 3 Academic Press, London, 1974).