## The Annals of Probability

### A comparison of scores of two protein structures with foldings

Tiefeng Jiang

#### Abstract

Let $\{X_i;\, i\geq 1\},\,\{Y_i;\,i\geq 1\},\,\{U, U_i;\, i\geq 1\}$ and $\{V, V_i;\, i\geq 1\}$ be four i.i.d. sequences of random variables. Suppose U and V are uniformly distributed on $[0,1]^3.$ For each realization of $\{U_j;\, 1\leq j\leq n\},\ \{X_{i,p};\break \, 1\leq p \leq n\}$ is constructed as a certain permutation of $\{X_p;\, 1\leq p\leq n\}$ for any $1\leq i \leq n.$ Also, $\{Y_{j,p};\, 1\leq p \leq n\}, 1\leq j\leq n,$ are constructed the same way, based on $\{Y_j\}$ and $\{V_j\}.$ For a score function F, we show that \begin{eqnarray*} W_n:= \max_{1\leq i, j,m \leq n}\sum_{p=1}^m F(X_{i,p},Y_{j, p}) \end{eqnarray*} 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.

#### Article information

Source
Ann. Probab., Volume 30, Number 4 (2002), 1893-1912.

Dates
First available in Project Euclid: 10 December 2002

https://projecteuclid.org/euclid.aop/1039548375

Digital Object Identifier
doi:10.1214/aop/1039548375

Mathematical Reviews number (MathSciNet)
MR1944009

Zentralblatt MATH identifier
1020.60015

#### Citation

Jiang, Tiefeng. A comparison of scores of two protein structures with foldings. Ann. Probab. 30 (2002), no. 4, 1893--1912. doi:10.1214/aop/1039548375. https://projecteuclid.org/euclid.aop/1039548375

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• MINNEAPOLIS, MINNESOTA 55455 E-MAIL: tjiang@stat.umn.edu.