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Dynamic properties of condensing particle systems

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Figure

Figure 2.1: Example configuration of the coupled dynamics. The ξin red and the second class particle is shown in blue
Figure 3.1:System size dependence of the background densitythe chipping model on a complete graph with RbgL (N) (3.30) for L = 2 N = 200, L = 10 N = 50,and L = 64 N = 320 as a function of w
Figure 4.1: → ∞ β= 1 (see Section 3.3 for details). The dotted black line shows the limit and N/L → ρbgtails withas L, N√b(4.8) for lattice sizesNon-monotone behaviour of the expected background density RL (N) L = 32 and L = 128; (a) (finite mean) power law tails with = 5, (b) log-normal tails with µ = 0 and σ = 1/2, and (c) almost exponential, which is monotone and non-decreasing.
Figure 4.2: Non-monotone behaviour of HLL(N) (4.12), which is the expected valueof the observable (4.9) rescaled by its limit; (A) power law tails w(n) ∼ n−b forL = 2 with b = 3, 1.75 and 1.35, where the latter is conjectured to be monotone(see Section 4.4); (B) log-normal tails (3.13) with µ = 0 and σ = 1/√2 for L = 2, = 32 and L = 128.
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Upper bounds via hitting times The chipping model

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