]. M. Abst70, I. A. Abramowitz, and . Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 1970.

D. [. Alili, M. Dufresne, and . Yor, Sur l'identité de Bougerol pour les fonctionnelles exponentielles du mouvement Brownien avec drift. In Exponential Functionals and Principal Values related to Brownian Motion. A collection of research papers, Biblioteca de la Revista Matematica, pp.3-14, 1997.

A. Amitai, I. Kupka, and D. Holcman, Mean first looping time of a rigid rod polymer, Preparation, 2011.

]. D. And87 and . André, Solution directe du problème résolu par M. Bertrand, C. R. Acad. Sci. Paris, vol.105, pp.436-437, 1887.

]. C. Bef91, J. Bélisle, and . Faraway, Winding angle and maximum winding angle of the two-dimensional random walk, J. Appl. Probab, vol.28, pp.717-726, 1991.

]. C. Bel86 and . Bélisle, Limit distribution of winding of planar of random walks, 1989.

]. C. Bel89 and . Bélisle, Windings of random walks, Ann. Probab, vol.17, pp.1377-1402, 1989.

J. Bertoin and W. Werner, Asymptotic windings of planar Brownian motion revisited via the Ornstein-Uhlenbeck process, Sém. Prob. XXVIII, Lect. Notes in Mathematics, vol.68, pp.138-152, 1994.
DOI : 10.2307/2371837

T. [. Bertoin, B. Fujita, M. Roynette, and . Yor, On a particular class of self-decomposable random variables: the duration of a Bessel excursion straddling an independent exponential time, Prob. Math. Stat, vol.26, pp.315-366, 2006.

]. P. Bil68 and . Billingsley, Convergence of Probability Measures, 1968.

]. P. Bil78 and . Billingsley, Probability and Measure, 1978.

]. P. Biy87, M. Biane, and . Yor, Valeurs principales associées aux temps locaux browniens, Bull. Sci. Math, vol.111, pp.23-101, 1987.

E. [. Biess, D. Korkotian, and . Holcman, Diffusion in a dendritic spine: The role of geometry, Physical Review E, vol.76, issue.2, 2007.
DOI : 10.1103/PhysRevE.76.021922

]. L. Bon90 and . Bondesson, Generalized gamma convolutions and complete monotonicity. Probab. Theory Related Fields, pp.181-194, 1990.

]. L. Bon92 and . Bondesson, Generalized gamma convolutions and related classes of distributions and densities, Lecture Notes in Statistics, vol.76, 1992.

G. [. Bentkus, M. Pap, and . Yor, Optimal bounds for Cauchy approximations for the winding distribution of planar Brownian motion, J. Theor. Probab, vol.16, issue.2, pp.259-279, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00104728

D. Burkholder, Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Advances in Mathematics, vol.26, issue.2, pp.182-205, 1977.
DOI : 10.1016/0001-8708(77)90029-9

J. [. Comtet, C. Desbois, and . Monthus, Asymptotic laws for the winding angles of planar Brownian motion, Journal of Statistical Physics, vol.23, issue.1-2, pp.433-440, 1993.
DOI : 10.1007/BF01052772

URL : https://hal.archives-ouvertes.fr/in2p3-00004900

C. [. Comtet, M. Monthus, and . Yor, Exponential functionals of Brownian motion and disordered systems, Journal of Applied Probability, vol.30, issue.02, pp.255-271, 1998.
DOI : 10.1080/17442509408833883

URL : https://hal.archives-ouvertes.fr/hal-00003990

[. Donati-martin, H. Matsumoto, and M. Yor, On positive and negative moments of the integral of geometric Brownian motions, Statistics & Probability Letters, vol.49, issue.1, pp.45-52, 2000.
DOI : 10.1016/S0167-7152(00)00029-8

[. Donati-martin, H. Matsumoto, and M. Yor, Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions, Publications of the Research Institute for Mathematical Sciences, vol.37, issue.3, pp.295-326, 2002.
DOI : 10.2977/prims/1145477226

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, 1994.

]. B. Drk96, M. Drossel, and . Kardar, Winding Angle Distributions for Directed Polymers, p.9610019, 1996.

]. D. Duf00 and . Dufresne, Laguerre Series for Asian and Other Options, Mathematical Finance, vol.10, issue.4, pp.407-428, 2000.

]. R. Dur82 and . Durrett, A new proof of Spitzer's result on the winding of 2-dimensional Brownian motion, Ann. Prob, vol.10, pp.244-246, 1982.

D. Dufresne and M. Yor, A two-dimensional extension of Bougerol's identity in law for the exponential functional of Brownian motion: the story so far, 2011.

]. P. Gar64 and . Garabedian, Partial Differential Equations, 1964.

]. I. Grr65, I. M. Gradshteyn, and . Ryzhik, Table of Integrals, Series and Products, 1965.

]. K. Itmk65, H. P. Itô, and . Mckean, Diffusion Processes and their Sample Paths, 1965.

B. [. James, M. Roynette, and . Yor, Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples, Probability Surveys, vol.5, issue.0, pp.346-415, 2008.
DOI : 10.1214/07-PS118

URL : https://hal.archives-ouvertes.fr/hal-00174743

]. I. Kash88, S. E. Karatzas, and . Shreve, Brownian Motion and Stochastic Calculus, 1988.

]. F. Kni81 and . Knight, Essentials of Brownian motion and diffusion, Math. Surv, vol.18, 1981.

[. Doussal, Y. Etzioni, and B. Horovitz, Winding of planar Gaussian processes, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.07, 2009.
DOI : 10.1088/1742-5468/2009/07/P07012

]. N. Leb63 and . Lebedev, Special Functions and their Applications, 1963.

]. N. Leb72 and . Lebedev, Special Functions and their Applications. Revised edition, translated from the Russian, 1972.

J. F. Le and . Gall, Some properties of planar Brownian motion . Ecole d'été de Saint-Flour XX, Lect. Notes in Mathematics, vol.1527, pp.112-234, 1990.

]. J. Legy87, L. Gall, and M. Yor, Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace, Prob. Th. Rel. Fields, vol.74, pp.617-635, 1987.

D. Dugué, OEuvres de Paul Lévy, Processus Stochastiques , Gauthier-Villars. 158 Random Functions: General Theory with Special Reference to Laplacian Random Functions by Paul Lévy, 1980.

H. Matsumoto and M. Yor, On Bougerol and Dufresne's identities for exponential Brownian functionals, Proc. Japan Acad, pp.152-155, 1998.
DOI : 10.3792/pjaa.74.152

]. H. May05, M. Matsumoto, and . Yor, Exponential functionals of Brownian motion, I: Probability laws at fixed time, Probab. Surveys, vol.2, pp.312-347, 2005.

]. R. May08, M. Mansuy, and . Yor, Aspects of Brownian Motion, 2008.

]. P. Mey82, M. Messulam, and . Yor, On D. Williams' " pinching method " and some applications, J. London Math. Soc, vol.26, pp.348-364, 1982.

L. [. Matsumoto, M. Nguyen, and . Yor, Subordinators related to the exponential functionals of Brownian bridges and explicit formulae for the semigroup of hyperbolic Brownian motions. Stochastic Processes and Related Topics, Proc. 12th Winter School at Stochastic Monographs, pp.213-235, 2002.

]. Y. Ochi85 and . Ochi, Limit theorems for a class of diffusion processes, Stochastics, vol.15, issue.4, pp.251-269, 1985.
DOI : 10.1080/17442508508833359

]. G. Pay00, . Pap, and M. Yor, The accuracy of Cauchy approximation for the windings of planar Brownian motion, Periodica Mathematica Hungarica, vol.41, pp.213-226, 2000.

]. J. Piy86, M. Pitman, and . Yor, Asymptotic Laws of planar Brownian Motion, Ann. Prob, vol.14, pp.733-779, 1986.

]. J. Piy03, M. Pitman, and . Yor, Infinitely divisible laws associated with hyperbolic functions. Canad, J. Math, vol.55, pp.292-330, 2003.

M. [. Pillay, A. Ward, R. Pierce, T. Straube, and . Kolokolnikov, Analysis of the mean first passage time for narrow escape problems, 2009.

R. [. Pastor, A. Zwanzig, and . Szabo, Diffusion limited first contact of the ends of a polymer: Comparison of theory with simulation, The Journal of Chemical Physics, vol.105, issue.9, p.3878, 1996.
DOI : 10.1063/1.472208

]. D. Rey99, M. Revuz, and . Yor, Continuous Martingales and Brownian Motion, 1999.

]. P. Rou53 and . Rouse, A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers, J. Chem. Phys, vol.21, p.1272, 1953.

J. Rudnick and Y. Hu, The winding angle distribution of an ordinary random walk, Journal of Physics A: Mathematical and General, vol.20, issue.13, pp.4421-4438, 1987.
DOI : 10.1088/0305-4470/20/13/042

J. Rudnick and Y. Hu, Winding angle of a self-avoiding random walk, Physical Review Letters, vol.60, issue.8, pp.712-715, 1988.
DOI : 10.1103/PhysRevLett.60.712

]. H. Sal94 and . Saleur, Winding-angle distribution for Brownian and selfavoiding walks, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat Interdiscip Topics, vol.50, pp.1123-1128, 1994.

]. Z. Shi98 and . Shi, Windings of Brownian motion and random walks in the plane. The Annals of Probability, pp.112-131, 1998.

]. F. Spi58 and . Spitzer, Some theorems concerning two-dimensional Brownian Motion, Trans. Amer. Math. Soc, vol.87, pp.187-197, 1958.

]. F. Spi64 and . Spitzer, Principles of random walk, 1964.

. A. Sshe06, Z. Singer, D. Schuss, B. Holcman, and . Eisenberg, Narrow Escape I, J. Stat. Phys, vol.122, issue.3, pp.437-463, 2006.

]. A. Ssh06a, Z. Singer, D. Schuss, and . Holcman, Narrow Escape II, J. Stat. Phys, vol.122, issue.3, pp.465-489, 2006.

]. A. Ssh06b, Z. Singer, D. Schuss, and . Holcman, Narrow Escape III, J. Stat. Phys, vol.122, issue.3, pp.491-509, 2006.

A. [. Schuss, D. Singer, and . Holcman, Narrow Escape: Theory and Applications to Cellular Microdomains, Proc. Nat. Acad. Sci., 41, pp.16098-16103, 2007.

A. Singer, Z. Schuss, and D. Holcman, Narrow escape and leakage of Brownian particles, Physical Review E, vol.78, issue.5, p.51111, 2008.
DOI : 10.1103/PhysRevE.78.051111

. A. Sss80, K. Szabo, Z. Schulten, and . Schulten, First passage time approach to diffusion controlled reactions, J. Chem. Phys, vol.72, pp.4350-4357, 1980.

]. O. Tho77 and . Thorin, On the infinite divisibility of the lognormal distribution, Scand. Actuar. J, vol.3, pp.121-148, 1977.

]. S. Vak11 and . Vakeroudis, On some infinite divisibility properties related with Bougerol's identity, Preparation, 2011.

M. [. Vakeroudis, D. Yor, and . Holcman, The Mean First Rotation Time of a Planar Polymer, Journal of Statistical Physics, vol.60, issue.104, 2011.
DOI : 10.1007/s10955-011-0227-6

URL : https://hal.archives-ouvertes.fr/hal-00553669

M. J. Ward and J. B. Keller, Strong Localized Perturbations of Eigenvalue Problems, SIAM Journal on Applied Mathematics, vol.53, issue.3, pp.770-798, 1993.
DOI : 10.1137/0153038

M. J. Ward, W. D. Henshaw, and J. B. Keller, Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems, SIAM Journal on Applied Mathematics, vol.53, issue.3, pp.799-828, 1993.
DOI : 10.1137/0153039

]. F. Wie84, Distribution of the angle of rotation for plane random walks. Physica A: Theoretical and statistical physics, pp.211-219, 1984.

]. G. Wif74, M. J. Wilemski, and . Fixman, Diffusion-controlled intrachain reactions of polymers. I Theory, J. Chem. Phys, vol.60, p.866, 1974.

D. Williams, A simple geometric proof of Spitzer's winding number formula for 2-dimensional Brownian motion, 1974.

M. Yor, Loi de l'indice du lacet Brownien, et distribution de Hartman-Watson, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.91, issue.1, pp.71-95, 1980.
DOI : 10.1007/BF00531612

M. Yor, Generalized meanders as limits of weighted Bessel processes, and an elementary proof of Spitzer's asymptotic result on Brownian windings, Studia Scient. Math. Hung, vol.33, pp.339-343, 1997.

M. Yor, Exponential Functionals of Brownian Motion and Related Processes, 2001.
DOI : 10.1007/978-3-642-56634-9