Originally Posted by

**akbar** Let $\displaystyle (\epsilon_1,...,\epsilon_{2n-1})$ be a random vector with the density:

$\displaystyle p(x_1,...,x_{2n-1})=c_n\exp(-\frac{1}{2}(x_1^2+\Sigma_{i=1}^{2n-2}(x_{i+1}-x_i)^2+x_{2n-1}^2))$

One can check this is a Gaussian vector with mean vector zero and $\displaystyle 2n-1\times 2n-1$ tridiagonal correlation matrix of the form:

$\displaystyle \left( \begin{array}{ccccc} 2 & -1 & 0 & ... & 0 \\ -1 & 2 & -1 & .& : \\ 0 & -1 & . & & 0 \\ : & .& & 2 & -1 \\ 0 & ...& 0 & -1 & 2 \end{array}\right)=M_{2n-1}$

(note: for some obscure reason, large parenthesis \left(, \right(, are not recognized by the forum editor...) (works for me ?!; otherwise you can use the environment "pmatrix", it's lighter to use)