Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $\Lambda_n = \{ -n,\ldots,n\}^2$ and let $\{X_i\}_{i\in \Lambda_n}$ be the family of $\mathbb{R}$-valued of random variables with the density proportional to

$\exp(-\sum_{i\sim j} |X_i - X_j|),$

where $i\sim j$ spans over $\Lambda_{n+1}$, $\sim$ denotes the neigbourhood in $Z^2$ and we assume that for $i \in \Lambda_{n+1} \setminus \Lambda_n$ we have $X_i =0 $ (boundary conditions). This model is known as the solid-on-solid (SOS) model.

My questions are:

  1. Does anybody know if there exists a proof of a upperbound for the height of this model?

  2. Does anybody know a "simple proof" of any upperbound? (I would be happy to have a weak estimate if it can be proved easily).

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.