Abstract
The computation of the second virial coefficient of a gas of anyons and the derivation of the probability P(n) for a planar brownian curve to wind n times around a given point are considered. The joint probability P(n, A) for the curve to wind n times and enclose an algebraic aera A is also studied and a lower bound on the arithmetic aera of the curve is given.
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References
J.M. Leinaas and J. Myrheim, Nuovo Cimento B37 (1977) 1
J.M. Leinaas, Nuovo Cimento A 47 (1978) 1
M. G. G. Laidlaw and C. M. de Witt, Phys. Rev. D3 (1971) 1375
F. Wilczek Phys. Rev. Letters Vol 49 (1982) 957
for a recent review on the subject see R. Mackenzie and F. Wilczek, Int. J. Mod. Phys. 3 (1988) 2827
Y.S. Wu, Proc. 2nd Symp. Foundations of Quantum Mechanics, Tokyo 1986, p 171-180 and Phys. Rev. Letters Vol 53 (1984) 111
H.J. de Vega and F.A. Schaposnik Phys. Rev. Letters Vol 56 (1986) 2564
S.K. Paul and A. Khare Phys. Lett. 174B (1986) 420
G. Semenoff Phys. Rev. Letters Vol 61 (1988) 517
Y-G. Chen, F. Wilczek, E. Witten and B.I. Halperin, Intern. J. Mod. Phys. B3 (1989) 1001
E. Witten Comm. Math. Phys. 121 (1989) 351
V.F.R. Jones Bull. AMS 12 (1986) 103
A. Comtet, Y. Georgelin and S. Ouvry J. Phys. A: Math. Gen. 22 (1989) 3917–3925
when spin effects are included see T. Blum, R. C. Hagen and S. Ramaswamy Phys. Rev. Lett 64 (1990) 709
A. Comtet, J. Desbois and S. Ouvry J. Phys. A: Math. Gen. 23 (1990) 3563
S. Ouvry, Nucl. Phys. B (Proc. Suppl.) 18B (1990) 250
B. Khan and G. E. Uhlenbeck, Physica 5 (1938) 399
D.P. Arovas, R. Schrieffer, F. Wilczek and A. Zee Nucl. Phys. B251 (1985) 117
J.S. Dowker, J. Phys. A18 (1985) 3521
S.F. Edwards Proc. Phys. Soc. 91 (1967) 9
F. W. Wiegel 1977 J. Chem. Phys. 67 n°2 469–472
This problem has been recently solved by M. Yor (private communication)
P. Levy, Processus stochastiques et mouvement brownien, Paris 1948
M. G. Brereton and C. Butler C 1987 J. Phys. A: Math. Gen. 20 3955–68
D. C. Khandekar and F. W. Wiegel F W 1988 J. Phys. A: Math. Gen. 21 563
B. Duplantier 1989 J. Phys. A: Math. Gen. 22 3033–3048
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© 1991 Plenum Press, New York
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Ouvry, S. (1991). Fractional Statistic and Planar Brownian Winding. In: Amar, M.B., Pelcé, P., Tabeling, P. (eds) Growth and Form. NATO ASI Series, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1357-1_42
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DOI: https://doi.org/10.1007/978-1-4684-1357-1_42
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