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Erschienen in:
Integral Representations of Certain Measures in the One-Dimensional Diffusions Excursion Theory Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Explicit Formulae in Probability and in Statistical Physics

verfasst von : Alain Comtet, Yves Tourigny

Erschienen in: In Memoriam Marc Yor - Séminaire de Probabilités XLVII

Verlag: Springer International Publishing

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Abstract

We consider two aspects of Marc Yor’s work that have had an impact in statistical physics: firstly, his results on the windings of planar Brownian motion and their implications for the study of polymers; secondly, his theory of exponential functionals of Lévy processes and its connections with disordered systems. Particular emphasis is placed on techniques leading to explicit calculations.

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Vorheriges Kapitel The Kolmogorov Operator and Classical Mechanics
Nächstes Kapitel Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space
Literatur
1.
P.W. Anderson, Absence of diffusion in a certain random lattice. Phys. Rev. 109, 1492–1505 (1958)CrossRef
2.
F. Baudoin, N. O’Connell, Exponential functionals of Brownian motion and class-one Whittaker functions. Ann. Inst. Henri Poincaré Probab. Stat. 47, 1096–1120 (2011)MATHMathSciNetCrossRef
3.
4.
5.
J. Bertoin, Lévy Processes (Cambridge University Press, Cambridge, 1996)MATH
6.
J. Bertoin, D. Dufresne, M. Yor, Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Rev. Mat. Iberoam. 29, 1307–1324 (2013)MATHMathSciNetCrossRef
7.
8.
J.-P. Bouchaud, A. Comtet, A. Georges, P. Le Doussal, Classical diffusion of a particle in a one-dimensional random force field. Ann. Phys. 201, 285–341 (1990)CrossRef
9.
C. Bouchiat, M. Mézard, Elasticity model of a supercoiled DNA molecule. Phys. Rev. Lett. 80, 1556–1559 (1998)CrossRef
10.
P. Bougerol, Examples de théorèmes locaux sur les groupes résolubles. Ann. Inst. H. Poincaré Sect. B (N.S.) 19, 403–432 (1983)
11.
P. Bougerol, J. Lacroix, Products of Random Matrices with Applications to Schrödinger Operators (Birkhaüser, Basel, 1985)MATHCrossRef
12.
P. Carmona, F. Petit, M. Yor, On the distribution and asymptotic results for exponential functionals of Lévy processes, in Exponential functionals and principal values related to Brownian motion. Bibl. Rev. Mat. Iberoamericana, Rev. Mat. Iberoamericana, Madrid, pp. 73–130 (1997)
13.
A. Comtet, J. Desbois, C. Monthus, Asymptotic laws for the winding angles of planar Brownian motion. J. Stat. Phys. 73, 433–440 (1993)MATHMathSciNetCrossRef
14.
15.
A. Comtet, C. Texier, Y. Tourigny, Supersymmetric quantum mechanics with Lévy disorder in one dimension. J. Stat. Phys. 145, 1291–1323 (2011)MATHMathSciNetCrossRef
16.
A. Comtet, C. Texier, Y. Tourigny, Lyapunov exponents, one-dimensional Anderson localization and products of random matrices. J. Phys. A Math. Theor. 46, 254003 (2013)MathSciNetCrossRef
17.
A. Comtet, C. Texier, Y. Tourigny, Products of random matrices and generalised quantum point scatterers. J. Stat. Phys. 140, 427–466 (2010)MATHMathSciNetCrossRef
18.
J. Desbois, C. Furtlehner, S. Ouvry, Random magnetic impurities and the Landau problem. Nucl. Phys. B 453 [FS], 759–776 (1995)
19.
B. Drossel, M. Kardar, Winding angle distributions for random walks and flux lines. Phys. Rev. E 53, 5861–5871 (1996)CrossRef
20.
D. Dufresne, The distribution of a perpetuity, with applications to risk theory and pension funding. Scan. Actuar. J. no. 1–2, 39–79 (1990)MathSciNetCrossRef
21.
22.
S.F. Edwards, Statistical mechanics with topological constraints I. Proc. Phys. Soc 91, 513–519 (1967)MATHCrossRef
23.
H.L. Frisch, S.P. Lloyd, Electron levels in a one-dimensional lattice. Phys. Rev. 120, 1175–1189 (1960)MATHCrossRef
24.
C. Garban, J.A. Trujillo-Ferreras, The expected area of the filled planar Brownian loop is π∕5. Commun. Math. Phys. 264, 797–810 (2006)MATHMathSciNetCrossRef
25.
G. Gavazzi, J.M. Wheatley, A.J. Schofield, Single particle motion in a random magnetic flux. Phys. Rev. E 47, 15170–15176 (1993)CrossRef
26.
H.K. Gjessing, J. Paulsen, Present value distribution with applications to ruin theory and stochastic equations. Stoch. Process. Appl. 71, 123–144 (1997)MATHMathSciNetCrossRef
27.
A. Grosberg, H. Frisch, Winding angle distribution for planar random walk, polymer ring entangled with an obstacle, and all that: Spitzer–Edwards–Prager–Frisch model revisited. J. Phys. A Math. Gen. 36, 8955 (2003)MATHMathSciNetCrossRef
28.
F. Hirsch, M. Yor, On the Mellin transforms of the perpetuity and the remainder variables associated to a subordinator. Bernoulli 19, 1350–1377 (2013)MATHMathSciNetCrossRef
29.
30.
31.
S. Kotani, On asymptotic behaviour of the spectra of a one-dimensional Hamiltonian with a certain random coefficient. Publ. RIMS Kyoto Univ. 12, 447–492 (1976)MATHMathSciNetCrossRef
32.
33.
J.-M. Luck, Systèmes désordonnés unidimensionels (Aléa, Saclay, 1992)
34.
H. Matsumoto, M. Yor, Exponential functionals of Brownian motion I: probability laws at fixed times. Probab. Surv. 2, 312–347 (2005)MATHMathSciNetCrossRef
35.
H. Matsumoto, M. Yor, Exponential functionals of Brownian motion II: some related diffusion processes. Probab. Surv. 2, 348–384 (2005)MATHMathSciNetCrossRef
36.
P. Messulam, M. Yor, On D. Williams’ “pinching method” and some applications. J. Lond. Math. Soc. s2–26, 348–364 (1982)
37.
38.
39.
B. Øksendal, Stochastic Differential Equations, 6th edn. (Springer, Berlin, 2010)
40.
L.A. Pastur, A. Figotin, Spectra of Random and Quasi-periodic Operators (Springer, Berlin, 1992)CrossRef
41.
P. Patie, Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes. Ann. Inst. H. Poincaré Probab. Stat. 45, 667–684 (2009)MATHMathSciNetCrossRef
42.
43.
S. Prager, H.L. Frisch, Statistical mechanics of a simple entanglement. J. Chem. Phys. 46, 1475–1483 (1967)CrossRef
44.
D. Revuz, M. Yor, Continuous Martingales and Brownian Motion (Springer, New-York, 1999)MATHCrossRef
45.
J. Rudnick, Y. Hu, The winding angle distribution of an ordinary random walk. J. Phys. A Math. Gen. 20, 4421–4439 (1987)MathSciNetCrossRef
46.
H. Saleur, Winding angle distribution for Brownian and self-avoiding walks. Phys. Rev. E 50, 1123–1130 (1994)CrossRef
47.
F. Spitzer, Some theorems concerning two-dimensional Brownian motions. Trans. Am. Math. Soc. 87, 187–197 (1958)MATHMathSciNet
48.
49.
W. Werner, Formule de Green, lacet brownien plan et aire de Lévy. Stoch. Process. Appl. 57, 225–245 (1995)MATHCrossRef
50.
M. Yor, Loi de l’indice du lacet Brownien et distributions de Hartman–Watson. Z. Wahrsch. Verw. Gebiete 53, 71–95 (1980)MATHMathSciNetCrossRef
51.
M. Yor, Exponential Functionals of Brownian Motion and Related Processes (Springer, Berlin, 2001)MATHCrossRef
Metadaten
Titel
Explicit Formulae in Probability and in Statistical Physics
verfasst von
Alain Comtet
Yves Tourigny
Copyright-Jahr
2015
Buch
In Memoriam Marc Yor - Séminaire de Probabilités XLVII

Print ISBN: 978-3-319-18584-2

Electronic ISBN: 978-3-319-18585-9

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-18585-9_22