Spatial increments of the KPZ fixed point with arbitrary compactly supported initial data are quantitatively comparable to Brownian motion on compacts, uniformly, enabling large deviation and entropy results.
Random Growth Models
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abstract
The link between a particular class of growth processes and random matrices was established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation. During the past ten years, this connection has been worked out in detail and led to an improved understanding of the large scale properties of one-dimensional growth models. The reader will find a commented list of references at the end. Our objective is to provide an introduction highlighting random matrices. From the outset it should be emphasized that this connection is fragile. Only certain aspects, and only for specific models, the growth process can be reexpressed in terms of partition functions also appearing in random matrix theory.
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Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
Spatial increments of the KPZ fixed point with arbitrary compactly supported initial data are quantitatively comparable to Brownian motion on compacts, uniformly, enabling large deviation and entropy results.