Scaling laws and mechanisms for growing systems... and monster trucks.
We investigate how systems expand over time while adhering to strict empirical regularities, specifically those exhibiting a power-law size-rank distribution. In this context, rank denotes an element's position in a list ordered by frequency, and size refers to the frequency of that element.
The first part of the talk focuses on the interplay between tokens (total elements, e.g., total words in a text, animals) and types (unique elements, e.g., distinct vocabulary, species). We demonstrate that any growing system preserving a power-law size-rank distribution must follow a well-defined relationship between types and tokens [1]. This implies that diversity growth in these systems is universally determined and independent of the underlying growth mechanism.
In the second part, we will introduce a generalization of Simon’s model to provide a mechanistic description of this constrained growth. While classic Simon’s model uses a fixed innovation rate to produce power-law distributions, it fails [2] in the critical regime where the distribution exponent is close to -1. We present a time-dependent innovation rate that allows for a correct, universal characterization of these systems across the full spectrum of scaling exponents [3].
[1] Rosillo-Rodes, P.; Hébert-Dufresne, L.; Dodds, P.; Phys. Rev. Research 8, L012029
[2] Dodds, P. et al.; Phys. Rev. E 95, 052301
[3] Rosillo-Rodes, P.; Zimmerman, J. W.; Hébert-Dufresne, L.; Dodds, P.; https://arxiv.org/abs/2604.13184
This IFISC Seminar will be broadcasted in the following zoom link: https://us06web.zoom.us/j/89027654460?pwd=Wg9TYMPqqP2ipfj2JVvEagmzaTw29c.1
Coffee and cookies will be served 15 minutes before the start of the seminar
Contact details:
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