ICTS:30045

Video URL

Integrable difference equations and orthogonal polynomials with respect to a deformed semicircle di…

Integrable difference equations and orthogonal polynomials with respect to a deformed semicircle distribution

(2024). Integrable difference equations and orthogonal polynomials with respect to a deformed semicircle distribution. SciVideos. https://www.youtube.com/live/325JhYC07ic

Integrable difference equations and orthogonal polynomials with respect to a deformed semicircle distribution. SciVideos, Oct. 29, 2024, https://www.youtube.com/live/325JhYC07ic 

          @misc{ scivideos_ICTS:30045,
            doi = {},
            url = {https://www.youtube.com/live/325JhYC07ic},
            author = {},
            keywords = {},
            language = {en},
            title = {Integrable difference equations and orthogonal polynomials with respect to a deformed semicircle distribution},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30045 see, \url{https://scivideos.org/icts-tifr/30045}}
          }
Jérémie Bouttier
Talk numberICTS:30045
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

I will revisit some integrable difference equations arising in the study of the distance statistics of random planar maps (discrete surfaces built from polygons). In a paper from 2003 written jointly with P. Di Francesco and E. Guitter, we conjectured a general formula for the so-called ``two-point function'' characterizing these statistics. The first proof of this formula was given much later in a paper from 2012 joint with E. Guitter, where we used bijective arguments and the combinatorial theory of continued fractions. I will present a new elementary and purely analytic proof of the result, obtained by considering orthogonal polynomials with respect to a polynomial deformation of the Wigner semicircle distribution. This talk is based on a work in progress with Sofia Tarricone.