Geometry from chaos or limit shapes in statistical mechanics

Abstract

This lecture will start with the statistical analysis of an unbiased coin tossing. The limit shape phenomenon occur for when the number of tossings is very large (tends to infinity). We will see that the limit shape here is 1/2 and will compute the structure of fluctuations near the limit shape. Then we will focus on discrete random surfaces. We will see that they will develop deterministic limit shape (emergent geometry) and how they fluctuate around it. No advance prior knowledge is required.