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Related Publication: Chatterjee, Sourav, Ron Peled, Yuval Peres, And Dan Romik. "Phase Transitions In Gravitational Allocation.".pdf

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Preview of Related publication: Chatterjee, Sourav, Ron Peled, Yuval Peres, and Dan Romik. "Phase transitions in gravitational allocation."
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Summary

Given a Poisson point process of unit masses in dimension d ≥ 3, Newtonian gravity partitions space into domains of attraction of equal volume. The diameters of these cells have exponential tails. The probability that mass exp(−Rγ) in a cell travels distance R decays like exp(−Rfd(γ)), where fd(γ) is a piecewise smooth function with discontinuities representing phase transitions. In dimension d = 3, the large deviation is due to a "distant attracting galaxy", while in dimensions d ≥ 5, it is due to a "wormhole" along which the star density increases monotonically. In dimension 4, a double phase transition occurs. The tail behavior of the distance from a star to a uniform point in its cell and a sharp lower bound for the tail probability of the cell's diameter are also determined.

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Given a Poisson point process of unit masses in dimension d ≥ 3, Newtonian gravity partitions space into domains of attraction of equal volume.

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  • File Format: PDF
  • File Size: 965 KB
  • Pages: 48
  • Language: EN
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