Asymptotic results for the Painlevé XXXIV equation
When dealing with linear differential equations, some of the most basic yet powerful tools are integral transforms such as the Fourier or Laplace transforms. Amongst their core features, they transform the original differential operators into multiplication, which in practice means turning the differential evolution in the original variables into explicitly solvable and simpler models in the Fourier space. [...]
A. R. Its, A. B. J. Kuijlaars, and J. Östensson. “Asymptotics for a special solution of the thirty fourth Painlevé equation”. In: Nonlinearity 22.7 (2009), pp. 1523–1558.
A. R. Its, A. B. J. Kuijlaars, and J. Östensson. “Critical edge behavior in unitary random matrix ensembles and the thirty-fourth Painlevé transcendent”. In: Int. Math. Res. Not. IMRN 9 (2008), pp. 1–67.
Guilherme L. F. Silva. “Contributions to the asymptotic theory of random particle systems and orthogonal polynomials”. Instituto de Ciências Matemáticas e de Computação - Universidade de São Paulo. Habilitation thesis (livre-docência), Dec. 2021.