Fredholm determinants

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1. [1] Ahlfors L.V., Complex Analysis, Internat. Ser. Pure Appl. Math., 3rd ed., McGraw-Hill, New York, 1979 Zbl0395.30001
2. [2] Brown R., A brief account of microscopical observations made in the months of June, July, and August, 1827, on the particles contained in the pollen of plants, etc., Philosophical Magazine, 1828, 4, 161–173 
3. [3] Cameron R.H., Martin W.T., The Wiener measure of Hilbert neighborhoods in the space of real continuous functions, Journal of Mathematics and Physics Mass. Inst. Tech., 1944, 23, 195–209 Zbl0060.29103
4. [4] Conrey J.B., The Riemann hypothesis, Notices Amer. Math. Soc., 2003, 50(3), 341–353 Zbl1160.11341
5. [5] Courant R., Differential and Integral Calculus, vol. 2, Wiley Classics Lib., John Wiley & Sons, New York, 1988 
6. [6] Courant R., Hilbert D., Methoden der Mathematischen Physik, Springer, Berlin, 1931 Zbl0001.00501
7. [7] Dyson F.J., Statistical theory of the energy levels of complex systems. I, J. Mathematical Phys., 1962, 3, 140–156 http://dx.doi.org/10.1063/1.1703773 Zbl0105.41604
8. [8] Dyson F.J., Fredholm determinants and inverse scattering problems, Comm. Math. Phys., 1976, 47(2), 171–183 http://dx.doi.org/10.1007/BF01608375 Zbl0323.33008
9. [9] Einstein A., Über die von der molekularkinetischen Theorie der Wärme gefordete Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys., 1905, 17, 549–560; reprinted in: Investigations on the Theory of the Brownian Movement, Dover, New York, 1956 http://dx.doi.org/10.1002/andp.19053220806 Zbl36.0975.01
10. [10] Fredholm I., Sur une classe d’équations fonctionelles, Acta Math., 1903, 27(1), 365–390 http://dx.doi.org/10.1007/BF02421317 Zbl34.0422.02
11. [11] Gardner C.S., Greene J.M., Kruskal M.D., Miura R.M., Methods for solving the Korteweg-deVries equation, Phys. Rev. Lett., 19(19), 1967, 1095–1097 http://dx.doi.org/10.1103/PhysRevLett.19.1095 Zbl1061.35520
12. [12] Jimbo M., Miwa T., Môri Y., Sato M., Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent, Phys. D, 1980, 1(1), 80–158 http://dx.doi.org/10.1016/0167-2789(80)90006-8 Zbl1194.82007
13. [13] Kato T., A Short Introduction to Perturbation Theory for Linear Operators, Springer, New York-Berlin, 1982 
14. [14] Lamb G.L., Jr., Elements of Soliton Theory, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 1980 Zbl0445.35001
15. [15] Lax P.D., Linear Algebra, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 1997 
16. [16] Lax P.D., Functional Analysis, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 2002 Zbl1009.47001
17. [17] Lévy P., Le Mouvement Brownien, Mémoir. Sci. Math., 126, Gauthier-Villars, Paris, 1954 
18. [18] McKean H.P., Jr., Stochastic Integrals, Probab. Math. Statist., Academic Press, New York-London, 1969 
19. [19] Mehta M.L., Random Matrices, 2nd ed., Academic Press, Boston, 1991 
20. [20] Munroe M.E., Introduction to Measure and Integration, Addison-Wesley, Cambridge, 1953 Zbl0050.05603
21. [21] Pöppe Ch., The Fredholm determinant method for the KdV equations, Phys. D, 1984, 13(1–2), 137–160 http://dx.doi.org/10.1016/0167-2789(84)90274-4 
22. [22] Tracy C.A., Widom H., Introduction to random matrices, In: Geometric and Quantum Aspects of Integrable Systems, Scheveningen, 1992, Lecture Notes in Phys., 424, Springer, Berlin, 1993, 103–130 http://dx.doi.org/10.1007/BFb0021444 
23. [23] Uhlenbeck G.E., Ornstein L.S., On the theory of the Brownian motion, Phys. Rev., 1930, 36, 823–841 http://dx.doi.org/10.1103/PhysRev.36.823 Zbl56.1277.03
24. [24] Weyl H., The Classical Groups, Princeton University Press, Princeton, 1939 
25. [25] Whittaker E.T., Watson G.N., A Course of Modern Analysis, 4th ed., Cambridge University Press, New York, 1962 
26. [26] Wiener N., Differential space, Journal of Mathematics and Physics Mass. Inst. Tech., 1923, 2, 131–174 
27. [27] Wigner E., On the distribution of the roots of certain symmetric matrices, Ann. of Math., 1958, 67, 325–326 http://dx.doi.org/10.2307/1970008 Zbl0085.13203