Level: MSci, MSc
Title: Asymptotics of Q-deformed binomial distributions
Supervisor:
Research Area: Dynamical Systems and Statistical Physics
Description:

Counting directed lattice paths with respect to length and area gives rise to Gaussian polynomials. It is known that the resulting distribution is after suitable rescaling described by a normal distribution, see the below reference. The purpose of this project is to refine this result, using methods from probability theory and/or asymptotic analysis.

Further Reading:
  • L. Takacs, Some asymptotic formulas for lattice paths, J. Stat. Plan. Inf. 14 (1986) 123–142.
Key Modules:
Other Information:

Some knowledge of enumerative and asymptotic combinatorics would be desirable.

Current Availability: Yes