Large energy fluctuations in Poisson fields under stochastic dynamics: application of permanental random point processes to analysis of Planck radiation

• Grant number: 16/25077-4
• Support type: Research Grants - Visiting Researcher Grant - International
• Duration: September 01, 2017 - November 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal researcher: Anatoli Iambartsev
• Grantee: Anatoli Iambartsev
• Visiting researcher: Valentin Zagrebnov
• Visiting researcher institution: Centre de Mathématiques et Informatique (CMI), France
• Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The project is aimed to study abrupt high fluctuations of radiation emitting by different type of sources. A unified nature is that these sources, although close to the well known black body radiation, are driven by different kind of stochastic dynamic. The project consists of two parts. The first part concerns the large deviations of the radiation fluctuations in general setting, where a driving input flow of the excitations and an output flow of the radiation of the system are arbitrary. In the second part is dedicated to study the examples of models where the both flows are specified. One of the main interest here are the systems similar to the black body sources. The Planck formula of radiations is considered as a main example in these studies. Moreover, constants in the Planck formula of the radiations will be estimated for the various systems and in particular for "acoustic black holes". Note that the both parts are integrated by a common background. They study the boson systems: either the photon Planck radiation, or the phonon Unruh-Hawkingradiation. Moreover, in the latter case a driving stochastic system is the Permanental Random Point Processes corresponding to perfect Bose-gas in the condensed state. (AU)