Let be a random vector with the density:
One can check this is a Gaussian vector with mean vector zero and the correlation matrix has an inverse given by the tridiagonal form:
By induction, one can also check that for all , which enables to obtain the normalizing constant using the usual formula for the Gaussian density (see for example Grimmett & Stirzaker).
Now for the question: how do you prove that there is a constant which does not depend on such that for all ?
By advance, thanks for your help.