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We generalize this statistic and derive an explicit formula for the number of Dyck paths of length 2 n according to the statistic “number of uu · · · udu ’s” (“number of udud ·
Schoof on the exponent of the group E ( F p) of F p-rational points, when a fixed elliptic curve E is defined over Q and the prime p tends to infinity..
The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity..
Abstract. The uniqueness of the non-negative fixed points of the associated smooth- ing transform is considered. New results on the asymptotic behaviour of the solutions near zero
The proof is largely based on the Costin-Lebowitz- Soshnikov argument and the asymptotic estimates for the expectation and variance of the number of eigenvalues in an interval..
It is expected that this model displays so-called self-organised critical behaviour as the lightning rate λ goes to zero.. If we start from any configuration with infinitely many
In particular, the result of this note has recently been used to prove Gaussian asymptotic behaviour for the Fourier transform of the two-point function for sufficiently
We can therefore invert the foregoing Laplace transform with respect to ν and we get the formula (4.9) corresponding to the case of the maximum functional... However, the
