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Statistical mechanics reveals how random interactions drive multi-state condensation. This study provides analytical insights into condensate fractions and their link to random games.

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Area of Science:

  • Statistical mechanics
  • Disordered systems
  • Game theory

Background:

  • Condensation phenomena can occur in systems with multiple possible states.
  • Understanding the statistical properties of these states is crucial for complex systems.
  • Random interactions are common in various scientific domains.

Purpose of the Study:

  • To investigate the static properties of condensation into multiple states using statistical mechanics.
  • To demonstrate the role of random interaction matrices in the statistics of condensate states.
  • To explore the connection between condensation and random zero-sum games.

Main Methods:

  • Employing methods from the statistical mechanics of disordered systems.
  • Developing a general framework for analyzing multi-state condensation.
  • Deriving analytical expressions for condensate properties.

Main Results:

  • Identified typical properties of random interaction matrices influencing condensate statistics.
  • Provided an analytical expression for the fraction of condensate states in the thermodynamic limit.
  • Confirmed results with the mean number of coexisting species in random tournament games.

Conclusions:

  • Random interaction matrices are key to understanding multi-state condensation.
  • The derived analytical expression offers a quantitative measure of condensation.
  • The study establishes a link between condensation phenomena and random zero-sum games.