|
|
|
|
References
|
|
| |
| 1. |
Betea D., Elliptically distributed lozenge tilings of a hexagon, arXiv: 1110.4176 |
| 2. |
Borodin A., Ferrari P. L., Prähofer M., Sasamoto T., Warren J., “Maximum of Dyson Brownian motion and non-colliding systems with a boundary”, Electron. Commun. Probab., 14 (2009), 486–494, arXiv: 0905.3989    |
| 3. |
Borodin A., Gorin V., Rains E. M., “$q$-distributions on boxed plane partitions”, Selecta Math. (N.S.), 16 (2010), 731–789, arXiv: 0905.0679  |
| 4. |
Borodin A., Rains E. M., “Eynard–Mehta theorem, Schur process, and their Pfaffian analogs”, J. Stat. Phys., 121 (2005), 291–317, arXiv: math-ph/0409059  |
| 5. |
Borodin A. N., Salminen P., Handbook of Brownian motion – facts and formulae, Probability and its Applications, 2nd ed., Birkhäuser Verlag, Basel, 2002 |
| 6. |
Dyson F. J., “A Brownian-motion model for the eigenvalues of a random matrix”, J. Math. Phys., 3 (1962), 1191–1198 |
| 7. |
Felder G., Varchenko A., “Three formulae for eigenfunctions of integrable Schrödinger operators”, Compositio Math., 107 (1997), 143–175, arXiv: hep-th/9511120 |
| 8. |
Forrester P. J., Log-gases and random matrices, London Mathematical Society Monographs Series, 34, Princeton University Press, Princeton, NJ, 2010 |
| 9. |
Gessel I., Viennot G., “Binomial determinants, paths, and hook length formulae”, Adv. Math., 58 (1985), 300–321 |
| 10. |
Ito M., Noumi M., “A generalization of the Sears–Slater transformation and elliptic Lagrange interpolation of type $BC_n$”, Adv. Math., 299 (2016), 361–380, arXiv: 1506.07267 |
| 11. |
Ito M., Noumi M., “Derivation of a $BC_n$ elliptic summation formula via the fundamental invariants”, Constr. Approx., 45 (2017), 33–46, arXiv: 1504.07108 |
| 12. |
Ito M., Noumi M., “Evaluation of the $BC_n$ elliptic Selberg integral via the fundamental invariants”, Proc. Amer. Math. Soc., 145 (2017), 689–703, arXiv: 1504.07317 |
| 13. |
Karlin S., McGregor J., “Coincidence probabilities”, Pacific J. Math., 9 (1959), 1141–1164 |
| 14. |
Katori M., “Determinantal martingales and noncolliding diffusion processes”, Stochastic Process. Appl., 124 (2014), 3724–3768, arXiv: 1305.4412 |
| 15. |
Katori M., Bessel processes, Schramm–Loewner evolution, and the Dyson model, Springer Briefs in Mathematical Physic, 11, Springer, Singapore, 2015 |
| 16. |
Katori M., “Elliptic determinantal process of type A”, Probab. Theory Related Fields, 162 (2015), 637–677, arXiv: 1311.4146 |
| 17. |
Katori M., “Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes”, J. Math. Phys., 57 (2016), 103302, 32 pp., arXiv: 1605.02931 |
| 18. |
Katori M., Tanemura H., “Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems”, J. Math. Phys., 45 (2004), 3058–3085, arXiv: math-ph/0402061 |
| 19. |
Katori M., Tanemura H., “Infinite systems of noncolliding generalized meanders and Riemann–Liouville differintegrals”, Probab. Theory Related Fields, 138 (2007), 113–156, arXiv: math.PR/0506187 |
| 20. |
Katori M., Tanemura H., “Noncolliding Brownian motion and determinantal processes”, J. Stat. Phys., 129 (2007), 1233–1277, arXiv: 0705.2460 |
| 21. |
Katori M., Tanemura H., “Zeros of Airy function and relaxation process”, J. Stat. Phys., 136 (2009), 1177–1204, arXiv: 0906.3666 |
| 22. |
Katori M., Tanemura H., “Non-equilibrium dynamics of Dyson's model with an infinite number of particles”, Comm. Math. Phys., 293 (2010), 469–497, arXiv: 0812.4108 |
| 23. |
Katori M., Tanemura H., “Noncolliding squared Bessel processes”, J. Stat. Phys., 142 (2011), 592–615, arXiv: 1008.0144 |
| 24. |
König W., O'Connell N., “Eigenvalues of the Laguerre process as non-colliding squared Bessel processes”, Electron. Comm. Probab., 6 (2001), 107–114 |
| 25. |
Koprucki T., Wagner H. J., “New exact ground states for one-dimensional quantum many-body systems”, J. Stat. Phys., 100 (2000), 779–790 |
| 26. |
Krattenthaler C., “Advanced determinant calculus: a complement”, Linear Algebra Appl., 411 (2005), 68–166, arXiv: math.CO/0503507 |
| 27. |
Levin B. Ya., Lectures on entire functions, Translations of Mathematical Monographs, 150, Amer. Math. Soc., Providence, RI, 1996 |
| 28. |
Liechty K., Wang D., “Nonintersecting Brownian bridges between reflecting or absorbing walls”, Adv. Math., 309 (2017), 155–208, arXiv: 1608.08712 |
| 29. |
Lindström B., “On the vector representations of induced matroids”, Bull. London Math. Soc., 5 (1973), 85–90 |
| 30. |
Macdonald I. G., “Affine root systems and Dedekind's $\eta$-function”, Invent. Math., 15 (1972), 91–143 |
| 31. |
Olshanetsky M. A., Perelomov A. M., “Quantum integrable systems related to Lie algebras”, Phys. Rep., 94 (1983), 313–404 |
| 32. |
Olver F. W. J., Lozier D. W., Boisvert R. F., Clark C. W. (eds.), NIST handbook of mathematical functions, U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC; Cambridge University Press, Cambridge, 2010 http://dlmf.nist.gov |
| 33. |
Revuz D., Yor M., Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften, 293, 3rd ed., Springer-Verlag, Berlin, 1999 |
| 34. |
Rosengren H., Schlosser M., “Elliptic determinant evaluations and the Macdonald identities for affine root systems”, Compos. Math., 142 (2006), 937–961, arXiv: math.CA/0505213 |
| 35. |
Schlosser M., A noncommutative weight-dependent generalization of the binomial theorem, arXiv: 1106.2112 |
| 36. |
Schlosser M., “Elliptic enumeration of nonintersecting lattice paths”, J. Combin. Theory Ser. A, 114 (2007), 505–521, arXiv: math.CO/0602260 |
| 37. |
Schlosser M., Yoo M., Weight-dependent commutation relations and combinatorial identities, arXiv: 1610.08680 |
| 38. |
Spohn H., “Interacting Brownian particles: a study of Dyson's model”, Hydrodynamic Behavior and Interacting Particle Systems (Minneapolis, Minn., 1986), IMA Vol. Math. Appl., 9, Springer, New York, 1987, 151–179 |
| 39. |
Sutherland B., “One-dimensional plasma as an example of a Wigner solid”, Phys. Rev. Lett., 35 (1975), 185–188 |
| 40. |
Takemura K., “On the eigenstates of the elliptic Calogero–Moser model”, Lett. Math. Phys., 53 (2000), 181–194, arXiv: math.QA/0002104 |
| 41. |
Tracy C. A., Widom H., “Nonintersecting Brownian excursions”, Ann. Appl. Probab., 17 (2007), 953–979, arXiv: math.PR/0607321 |
| 42. |
Warnaar S. O., “Summation and transformation formulas for elliptic hypergeometric series”, Constr. Approx., 18 (2002), 479–502, arXiv: math.QA/0001006 |
| 43. |
Whittaker E. T., Watson G. N., A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996 |
