Extreme Value Statistics: How Big is Big?

Seminar
Colloquium
QUEST Center event
No
Speaker
David A. Kessler
Date
14/03/2022 - 14:00 - 12:30Add to Calendar 2022-03-14 12:30:00 2022-03-14 14:00:00 Extreme Value Statistics: How Big is Big?     We present an introduction to extreme value statistics, the statistics of the largest of a series of random numbers.  We first discuss the case of independent variables drawn from a given distribution and show the origin of the 3 universality classes for long series, Gumbel (for exponentially decaying distributions), Frechet (for distributions that decay as a power-law) and Weibull (for bounded distributions).  We show how in practice Gumbel is a poor approximation and how to get more accurate formulas. We then turn to correlated variables, in particular those generated by a Langevin equation.  We show that the statistics of the continuously monitored process are different than those are any discrete sampling of the data, and for long-time series and restoring forces that increase with distance, the correlations eventually become irrelevant and the extreme value statistics approach those of an uncorrelated series of the same length drawn from the equilibrium distribution.   Physics Building 203, Room 221 and https://us02web.zoom.us/j/89236785442 Department of Physics physics.dept@mail.biu.ac.il Asia/Jerusalem public
Place
Physics Building 203, Room 221 and https://us02web.zoom.us/j/89236785442
Abstract

 

  We present an introduction to extreme value statistics, the statistics of the largest of a series of random numbers.  We first discuss the case of independent variables drawn from a given distribution and show the origin of the 3 universality classes for long series, Gumbel (for exponentially decaying distributions), Frechet (for distributions that decay as a power-law) and Weibull (for bounded distributions).  We show how in practice Gumbel is a poor approximation and how to get more accurate formulas. We then turn to correlated variables, in particular those generated by a Langevin equation.  We show that the statistics of the continuously monitored process are different than those are any discrete sampling of the data,
and for long-time series and restoring forces that increase with distance, the correlations eventually become irrelevant and the extreme value statistics approach those of an uncorrelated series of the same length drawn from the equilibrium distribution.

 

Last Updated Date : 13/03/2022