n=500: sup|CDF diff| on grid = 0.0168 at z=1.0; grid E[max]/sqrt(beta n) = 1.2469 vs excursion (same grid) 1.2533; sqrt(beta n)*(gap) = 0.110
n=1000: sup|CDF diff| on grid = 0.0187 at z=1.1; grid E[max]/sqrt(beta n) = 1.2427 vs excursion (same grid) 1.2533; sqrt(beta n)*(gap) = 0.258
n=2000: sup|CDF diff| on grid = 0.0176 at z=1.1; grid E[max]/sqrt(beta n) = 1.2424 vs excursion (same grid) 1.2533; sqrt(beta n)*(gap) = 0.373
n=4000: sup|CDF diff| on grid = 0.0146 at z=1.1; grid E[max]/sqrt(beta n) = 1.2439 vs excursion (same grid) 1.2533; sqrt(beta n)*(gap) = 0.454
n=8000: sup|CDF diff| on grid = 0.0115 at z=1.1; grid E[max]/sqrt(beta n) = 1.2458 vs excursion (same grid) 1.2533; sqrt(beta n)*(gap) = 0.517
