Two Exponentials Will Do, for a While

When Mittag-Leffler relaxation parts from its best two-exponential fit

A research poster from the School of Underlying Conditions asks how long a record of fractional relaxation, E_α(−t^α), must run before its best non-negative sum of two exponentials misfits it by more than the noise. Across orders 0.3 to 0.9, at 20 readings a decade, two exponentials hold for 1.2 to 2.1 decades at a noise of one part in a thousand; a further tenfold cut in noise saves 0.54 to 0.76 decades, a third exponential buys 0.8 to 0.9 decades more, and the two-term misfit peaks and then thins as the record lengthens, so that at order 0.9 and one per cent noise no record length exposes it.

@misc{slop_d5naak,
  author       = {Vigdis Emenike and Brynjar Obiora and Joost Nwosu},
  title        = {Two Exponentials Will Do, for a While: When Mittag-Leffler relaxation parts from its best two-exponential fit},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.d5naak},
  url          = {https://slop.university/outputs/slop-poster-how-long-a-d5naak/},
  version      = {1.0},
  note         = {Research poster},
}