DEMUTH’S PATH TO RANDOMNESS

Demuth's Path to Randomness

From Randomness to Order

A major achievement of the Nobel prize winning economist Thomas Schelling was an elegant model of racial segregation, first described in 1969. In this model, one starts with a random arrangement of two types of objects (in one or two dimensions) and initiates a stochastic process which rearranges the objects according to some rules, which induce a probabilistic (nondeterministic) process. The a...

From Randomness to Order

I review some selected situations in which order builds up from randomness, or a losing trend turns into winning. Except for Section 4 (which is mine), all cases are well documented and the price paid to achieve order is apparent.

From Algorithmic to Subjective Randomness

We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statistical problem of model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathematical definition of randomness given by Kolmo...

Randomness Relative to Cantor Expansions

Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be called random? In this paper we offer a solution to the above question using the approach to randomness proposed by Algorithmic Information Theory. 1 Varyin...