## Abstract

Let {X_{i}; i ≥ 1}, {Y_{i}; i ≥ 1}, {U, U_{i}; i ≥ 1} and {V, V_{i}; i ≥ 1} be four i.i.d, sequences of random variables. Suppose U and V are uniformly distributed on [0, 1]^{3}. For each realization of {U_{j}; 1 ≤ j ≤ n}, {X_{i,p}; 1 ≤ p ≤ n} is constructed as a certain permutation of {X_{p}; 1 ≤ p ≤ n} for any 1 ≤ i ≤ n. Also, {Y_{j, p}; 1 ≤ p ≤ n}, 1 ≤ j ≤ n, are constructed the same way, based on {Y_{j}} and {V_{j}}. For a score function F, we show that W_{n} := max_{1≤i,j,m≤n} Σ_{p=1}^{m} F (X_{i,p}, Y_{j,p}) has an asymptotic extreme distribution with the same parameters as in the one-dimensional case. This model is constructed for a comparison of scores of protein structures with foldings.

Original language | English (US) |
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Pages (from-to) | 1893-1912 |

Number of pages | 20 |

Journal | Annals of Probability |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - Oct 2002 |

## Keywords

- Chen-Stein method and large deviations
- Maxima