Contextuality scenarios arising from networks of stochastic processes

• URL: http://arxiv.org/abs/2006.12432v1
• Date: Mon, 22 Jun 2020 16:57:52 GMT
• Title: Contextuality scenarios arising from networks of stochastic processes
• Authors: Rodrigo Iglesias, Fernando Tohm\'e, Marcelo Auday
• Abstract summary: An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. We present a different and classical source of contextual empirical models: the interaction among many processes. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations are coherent, in the sense that the distribution on a face of a simplex coincides with the marginal of the distribution over the entire simplex. An empirical model is said contextual if its distributions cannot be obtained marginalizing a joint distribution over X. Contextual empirical models arise naturally in quantum theory, giving rise to some of its counter-intuitive statistical consequences. In this paper we present a different and classical source of contextual empirical models: the interaction among many stochastic processes. We attach an empirical model to the ensuing network in which each node represents an open stochastic process with input and output random variables. The statistical behavior of the network in the long run makes the empirical model generically contextual and even strongly contextual.

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