# Competing Particle Systems and the Ghirlanda-Guerra Identities

@article{Arguin2007CompetingPS, title={Competing Particle Systems and the Ghirlanda-Guerra Identities}, author={Louis-Pierre Arguin}, journal={Electronic Journal of Probability}, year={2007}, volume={13}, pages={2101-2117} }

Competing particle systems are point processes on the real line whose configurations $X$ can be ordered decreasingly and evolve by increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and quantified by a matrix $Q=\{q_{ij}\}$. Quasi-stationary systems are those for which the law of $(X,Q)$ is invariant under the evolution up to translation of $X$. It was conjectured by Aizenman and co-authors that the matrix $Q$ of robustly quasi… Expand

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