Nearest neighbour spacing distribution in the GUE
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Power series expansion of the d.e. about the origin
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Power series expansion of nn(s) about s=0
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Numerical solution of the d.e., calculation
of the mean and comparison with power series
expansion
Here the power series solution at s=1.1 is used as the
initial condition
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Here the numerical solution is integrated to
determine the mean of the distrubution
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Next the numerical solution is compared to the power series solution
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The function nn(s) can be tabulated
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Comparison with data from the GUE
Code to generate GUE matrices and plot empirical value of nn(s) (output
suppressed)
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Calculation of theoretical curve for nn(s) and comparison with numerical data
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Comparison with data from zeros of Riemann
zeta function for 10^6 zeros about the 10^20
zero, 10^6 zero and first zero
Here we read in the data as a list. The data gives the number
of zeros in the intervals [j*.05, (j+1)*.05) (j=0,...40). The third,
fourth and fifth columns contain the data for zeros about
zero 1, zero 10^6 and zero 10^20 respectively. The theoretical
value of nn(s) is plotted from the Table t.
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