2009/04/07 by Nathalie Krell, Krell, Nathalie, Alain Rouault +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.48550/arxiv.0904.1167
openalex publication_date 2009/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≤ 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.