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• W2951135447 abstract "The main focus of this work is the asymptotic behavior of mass-conservative homogeneous fragmentations. Considering the logarithm of masses makes the situation reminiscent of branching random walks. The standard approach is to study {bf asymptotical} exponential rates. For fixed $v > 0$, either the number of fragments whose sizes at time $t$ are of order $e^{-vt}$ is exponentially growing with rate $C(v) > 0$, i.e. the rate is effective, or the probability of presence of such fragments is exponentially decreasing with rate $C(v) < 0$, for some concave function $C$. In a recent paper, N. Krell considered fragments whose sizes decrease at {bf exact} exponential rates, i.e. whose sizes are confined to be of order $e^{-vs}$ for every $s leq t$. In that setting, she characterized the effective rates. In the present paper we continue this analysis and focus on probabilities of presence, using the spine method and a suitable martingale." @default.
• W2951135447 created "2019-06-27" @default.
• W2951135447 creator A5015430867 @default.
• W2951135447 creator A5076842871 @default.
• W2951135447 date "2009-04-07" @default.
• W2951135447 modified "2023-09-27" @default.
• W2951135447 title "Martingales and Rates of Presence in Homogeneous Fragmentations" @default.
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• W2951135447 hasPublicationYear "2009" @default.
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