Speaker :
| Nikolaos Zygouras (University of Warwick) |
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Title :
| Structures around the Kardar-Parisi-Zhang equation and universality. |

Time :
| 2018-03-29 (Thu) 15:00 - 16:00 |

Place : | Auditorium, 6 Floor, Institute of Mathematics (NTU Campus) |

Abstract: |
It was proposed by Kardar, Parisi and Zhang in the 1980s that a large class of randomly growing interfaces exhibit universal fluctuations described mathematically by a nonlinear stochastic partial differential equation, which is now known as the Kardar-Parisi-Zhang or KPZ equation. Examples of physical systems which fall in this class are percolation of liquid in porous media, growth of bacteria colonies, currents in one dimensional traffic or liquid systems, liquid crystals etc.
Surprisingly the fluctuations of such random interfaces are governed by exponents and distributions that differ from the predictions given by the classical central limit theorem and in dimension one are linked to laws emerging from random matrix theory. In higher dimension, however, even prediction on exponents elude us. In this talk I will review some of our current understanding on the one dimensional KPZ and the methods around it and show some first steps in dimension two. |