### Citations

280 | Probability Metrics and the Stability of Stochastic Models. - Rachev - 1991 |

232 |
Fracture of Brittle Solids,
- Lawn
- 1993
(Show Context)
Citation Context ...Fragmentation models, fixed point, contraction method, Mellin transform. 1 Introduction Fragmentation is a widely studied phenomena [12] with applications ranging from conventional fracture of solids =-=[6]-=- and collision induced fragmentation in atomic nuclei/ aggregates [1] to seemingly unrelated fields such as disordered systems [4] and geology. Fragmentation processes are also relevant to spin glasse... |

97 | A note on the height of binary search trees - Devroye - 1986 |

73 | A general limit theorem for recursive algorithms and combinatorial structures. - Neininger, Ruschendorf - 2004 |

71 | The contraction method for recursive algorithms.
- Rosler, Ruschendorf
- 2001
(Show Context)
Citation Context ...[14]. Rachev and Rï£¡schendorf [9] added several useful extensions. General contraction theorems and multivariate extensions were added by Rï£¡sler [11], and Neininger [8]. Rï£¡sler and Rï£¡schendorf =-=[13]-=- provide a valuable survey. Recently general contraction theorems and multivariate extensions were added, with continuous parameter, by Janson and Neininger [16]. By the recursive decomposition of the... |

70 | Branching processes in the analysis of the heights of trees. - Devroye - 1987 |

50 | Probability metrics and recursive algorithms
- Rachev, Rüschendorf
- 1995
(Show Context)
Citation Context ...s then verified by showing convergence of the distribution function to that of the guessed limit in some metric space. The contraction method was introduced by Rï£¡sler [14]. Rachev and Rï£¡schendorf =-=[9]-=- added several useful extensions. General contraction theorems and multivariate extensions were added by Rï£¡sler [11], and Neininger [8]. Rï£¡sler and Rï£¡schendorf [13] provide a valuable survey. Re... |

35 | On a multivariate contraction method for random recursive structures with applications to Quicksort.
- Neininger
- 2001
(Show Context)
Citation Context ...thod was introduced by Rï£¡sler [14]. Rachev and Rï£¡schendorf [9] added several useful extensions. General contraction theorems and multivariate extensions were added by Rï£¡sler [11], and Neininger =-=[8]-=-. Rï£¡sler and Rï£¡schendorf [13] provide a valuable survey. Recently general contraction theorems and multivariate extensions were added, with continuous parameter, by Janson and Neininger [16]. By t... |

22 | Ideal metrics in the problem of approximating the distri-butions of sums of independent random variables - Zolotarev - 1977 |

7 |
Stable distributions in stochastic fragmentation
- Krapivsky, Ben-Naim, et al.
- 2004
(Show Context)
Citation Context ...networks and genetic population. We investigate two classes of stochastic fragmentation processes. In section 2 we consider a random fragmentation process introduced by Krapivsky, Ben-Naim and Grosse =-=[5]-=- where fragmentation stops stochastically, with a probability q of further fragmentation that not depend on the mass x of the fragment. In section 3, we consider the random fragmentation process inves... |

7 |
Random sequential bisection and its associated binary tree
- Sibuya, Itoh
- 1987
(Show Context)
Citation Context ... fragments have an intrinsic size scale below which the fragmentation probability becomes negligible. If p(s) = 1Is≥1, m = 2 and ξ is uniform on [0, 1], this model has been studied by Sibuya and Itoh =-=[15]-=-. Recently Janson and Neininger [16] studied the general case where p(s) = 1Is≥1, m ≥ 2 and the support of the distribution of (ξ1, ξ2, · · · , ξm) on the standard simplex has an interior point. In ou... |

6 | The size of random fragmentation trees
- Janson, Neininger
(Show Context)
Citation Context ...astically, with a probability q of further fragmentation that not depend on the mass x of the fragment. In section 3, we consider the random fragmentation process investigated by Janson and Neininger =-=[16]-=-, where splitting probability is, by nature, fragments length dependent. A particle having some mass x is broken, with probability p(x) = 1 − e −x , into two pieces. The mass is distributed among the ... |

2 |
Statistical Models for the Fracture of Disordered
- RednerFor
- 1990
(Show Context)
Citation Context ...e fixed-point equation is easily verified to be Gaussian. Keywords: Fragmentation models, fixed point, contraction method, Mellin transform. 1 Introduction Fragmentation is a widely studied phenomena =-=[12]-=- with applications ranging from conventional fracture of solids [6] and collision induced fragmentation in atomic nuclei/ aggregates [1] to seemingly unrelated fields such as disordered systems [4] an... |

1 |
On the analysis of stochastic divide and conquer algorithms
- Rï£¡sler
- 2001
(Show Context)
Citation Context .... The contraction method was introduced by Rï£¡sler [14]. Rachev and Rï£¡schendorf [9] added several useful extensions. General contraction theorems and multivariate extensions were added by Rï£¡sler =-=[11]-=-, and Neininger [8]. Rï£¡sler and Rï£¡schendorf [13] provide a valuable survey. Recently general contraction theorems and multivariate extensions were added, with continuous parameter, by Janson and N... |

1 |
A limit theorem for “Quicksort
- Rï£¡sler
- 1991
(Show Context)
Citation Context ...tribution of N∗(x). The guess is then verified by showing convergence of the distribution function to that of the guessed limit in some metric space. The contraction method was introduced by Rï£¡sler =-=[14]-=-. Rachev and Rï£¡schendorf [9] added several useful extensions. General contraction theorems and multivariate extensions were added by Rï£¡sler [11], and Neininger [8]. Rï£¡sler and Rï£¡schendorf [13]... |