For a stationary AR(1) process, the expected value of the maximum of short contiguous segments is maximized at negative serial correlation, and the variance of the maximum increases monotonically with correlation.
Mean Width of a Regular Simplex
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abstract
The mean width is a measure on n-dimensional convex bodies. An integral formula for the mean width of a regular n-simplex appeared in the electrical engineering literature in 1997. As a consequence, expressions for the expected range of a sample of n+1 normally distributed variables, for n<=6, carry over to widths of regular n-simplices. As another consequence, precise asymptotics for the mean width become available as n->infty.
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Moments of Maximum: Segment of AR(1)
For a stationary AR(1) process, the expected value of the maximum of short contiguous segments is maximized at negative serial correlation, and the variance of the maximum increases monotonically with correlation.