Random exponentials and Dickmann’s laws: survey and applications

The Dickmann’s law was discovered in the number theory (statistics of the natural numbers with a small prime factors). The Derrida’s model of the random energies demonstrated the physical phase transitions of the second type. These models are from the completely different areas, however they have the same background and many similarities. The talk will contain the discussion of such similarities and the numerous applications, in particular, to the cell growth model.