Feller property of the multiplicative coalescent with linear deletion

Preprint, Other literature type English OPEN
Ráth, Balázs;

We modify the definition of Aldous’ multiplicative coalescent process (Ann. Probab. 25 (1997) 812–854) and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of cl... View more
  • References (18)
    18 references, page 1 of 2

    [1] L. Addario-Berry, N. Broutin and C. Goldschmidt. The continuum limit of critical random graphs. Probab. Theo. and Rel. Fields 152.3-4, 367- 406, 2012.

    [2] D. Ahlberg, H. Duminil-Copin, G. Kozma and V. Sidoravicius. Sevendimensional forest fires. Ann. de l'Institut Henri Poincar´e, Probabilit´es et Statistiques, 51(3), 862-866, 2015.

    [3] D.J. Aldous. Brownian Excursions, Critical Random Graphs and the Multiplicative Coalescent. Annals of Probability 25: 812-854, 1997.

    [4] D.J. Aldous and V. Limic. The entrance boundary of the multiplicative coalescent. Electronic Journal of Probability 3, paper 3, 59 pp. (1998)

    [5] D. J. Aldous. The percolation process on a tree where infinite clusters are frozen. Math. Proc. Cambridge Philos. Soc., 128(3):465-477, 2000.

    [6] J. van den Berg, D. Kiss and P. Nolin. Two-dimensional volumefrozen percolation: deconcentration and prevalence of mesoscopic clusters. arXiv:1512.05335, 2015.

    [7] J. van den Berg, B. N. B. de Lima, P. Nolin. A percolation process on the square lattice where large finite clusters are frozen. Rand. Struct. and Alg. 40.2, 220-226, 2012.

    [8] J. van den Berg, P. Nolin. Two-dimensional volume-frozen percolation: exceptional scales. (to appear in Ann. Appl. Probab.), arXiv:1501.05011, 2015.

    [9] J. van den Berg, B. T´oth. A signal-recovery system: asymptotic properties, and construction of an infinite-volume process. Stoch. Proc. and Appl. 96.2, 177-190, 2001.

    [10] S. Bhamidi, R. van der Hofstad, and J. van Leeuwaarden. Scaling limits for critical inhomogeneous random graphs with finite third moments. Electron. J. Probab. 15(54), 1682-1702, 2010.

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