 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2007/p/4/d/solution

A^{T}

1/4, q, \dots, q, ϵ

. They too are disjoint and have one eigenvalue each. The disc centered at

n

therefore improves the final bound to

n - ϵ \leq λ_{n} \leq n + ϵ .

It selects the same eigenvalue as before because all other discs lie a fixed positive distance from the disc centered at

n

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