• Corpus ID: 245006258

Tightness of discrete Gibbsian line ensembles

  title={Tightness of discrete Gibbsian line ensembles},
  author={Christian Serio},
A discrete Gibbsian line ensemble $\mathfrak{L} = (L_1,\dots,L_N)$ consists of $N$ independent random walks on the integers conditioned not to cross one another, i.e., $L_1 \geq \cdots \geq L_N$. In this paper we provide sufficient conditions for convergence of a sequence of suitably scaled discrete Gibbsian line ensembles $f^N = (f_1^N,\dots,f_N^N)$ as the number of curves $N$ tends to infinity. Assuming log-concavity and a KMT-type coupling for the random walk jump distribution, we prove that…