Biorthogonal polynomials for 2-matrix models with semiclassical potentials
| dc.creator | Bertola, M | |
| dc.date | 2006-05-03 | |
| dc.date.accessioned | 2026-07-07T09:29:45Z | |
| dc.date.available | 2026-07-07T09:29:45Z | |
| dc.description | We consider the biorthogonal polynomials associated to the two-matrix model where the eigenvalue distribution has potentials V_1,V_2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals (hard-edges). We show that these polynomials satisfy certain recurrence relations with a number of terms d_i depending on the number of hard-edges and on the degree of the rational functions V_i'. Using these relations we derive Christoffel-Darboux identities satisfied by the biorthogonal polynomials: this enables us to give explicit formulae for the differential equation satisfied by d_i+1 consecutive polynomials, We also define certain integral transforms of the polynomials and use them to formulate a Riemann-Hilbert problem for (d_i+1) x (d_i+1) matrices constructed out of the polynomials and these transforms. Moreover we prove that the Christoffel-Darboux pairing can be interpreted as a pairing between two dual Riemann-Hilbert problems. | |
| dc.description | 47 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0605008 | |
| dc.identifier | http://arxiv.org/abs/nlin/0605008 | |
| dc.identifier | J. Approx. Theory 144 (2007) no. 2, 162-212 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157900 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Biorthogonal polynomials for 2-matrix models with semiclassical potentials | |
| dc.type | text |