Mean field mutation dynamics and the continuous Luria-Delbrück distribution
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Published on: November 28, 2019
Eugene Kashdan1, Lorenzo Pareschi
1Applied Mathematics Department, Tel Aviv University, Israel. ekashdan@post.tau.ac.il
Abstract:
The Luria-Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.
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