Asymptotic fluctuations of a particle system with singular interaction
Tài liệu tham khảo
Aldous, 1978, Stopping times and tightness, Ann. Probab., 6, 335, 10.1214/aop/1176995579
Billingsley, 1968
Cépa, 1997, Diffusing particles with electrostatic repulsion, Probab. Theory Related Fields, 107, 429, 10.1007/s004400050092
Chan, 1992, The Wiegner semi-circle law and the eigenvalues of matrix-valued diffusions, Probab. Theory Related Fields, 93, 249, 10.1007/BF01195231
Dawson, 1983, Critical dynamics and fluctuations for a mean-field model of cooperative behavior, J. Statist. Phys., 31, 30, 10.1007/BF01010922
Dawson, 1989, Stable hydrodynamic limit fluctuations of a critical branching particle system in a random medium, Ann. Probab., 17, 1083, 10.1214/aop/1176991258
Duvillard, T.C., Fluctuations de la loi spectrale des grandes matrices aléatoires, Ann. Inst. H. Poincaré, to appear.
Dyson, 1962, A Brownian motion model for the eigenvalues of a random matrix, J. Math. Phys., 3, 1191, 10.1063/1.1703862
Johansson, 1998, On Fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J., 91, 151, 10.1215/S0012-7094-98-09108-6
Karatzas, 1991
Mehta, 1967
Mitoma, 1983, Tightness of probabilities on C([0,1];S′) and D([0,1];S′), Ann. Probab., 11, 989, 10.1214/aop/1176993447
Rogers, 1993, Interacting Brownian particles and the Wigner law, Probab. Theory Related Fields, 95, 557, 10.1007/BF01196734
Spohn, H., 1987. Interacting Brownian particles: a study of Dyson's model. Hydrodynamic Behavior and Interacting Particle Systems, Mathematical Applications, IMA Vol. 9. Minneapolis, MN, 1986, Springer, New York, Berlin, pp. 151–179.
Spohn, 1998, Dyson's model of interacting Brownian motions at arbitrary coupling strength, Markov Process. Related Fields, 4, 649
Treves, 1967