Concentration inequalities

Ponente(s): Jordan Moles ., Edgardo Ugalde Saldaña Jean-René Chazottes

In probability theory, concentration inequalities provide bounds on how a random variable deviates from some value. The law of large number of classical probability theory states that sums of independent random variables are close to their expectation with a large probability. Such sums are the most basic examples of random variables concentrated around their mean. Recent results show that such behavior is shared by other functions of independent random variables. I will introduce concentration inequalities with some examples from the simplest independent and identically distributed random variables (with the coin flipping) generalizing with Markov chains (with the Ehrenfest model) until recent results based on chains with complete connections.