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Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices
Harmonic Maaß -Jacobi forms degree 1 higher rank indices
2011/1/21
We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi grou...
Spectra of Random Hermitian Matrices with a Small-Rank External Source: The critical and near-critical regimes
Spectra of Random Hermitian Matrices Small-Rank External Source
2010/11/24
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, whi...
Bak--Sneppen type models and rank-driven processes
Bak--Sneppen type models rank-driven processes
2010/11/10
We analyse a surprising connection between Bak--Sneppen type models and much simpler Markov processes, which we call rank-driven processes (RDPs).
Let p(n) denote the number of partitions of n . Ramanujan's partition congruences are p(5n + 4) , p(7n + 5) and p(11n + 6) = mod 5, 7, and 11, respectively. These have been proved in number of ways. ...