Van Assche, Walter Orthogonal polynomials, Toda lattices and Painlevé equations. (English) Zbl 1498.33016 Physica D 434, Article ID 133214, 9 p. (2022). Reviewer: Christoph Koutschan (Linz) MSC: 33D45 PDFBibTeX XMLCite \textit{W. Van Assche}, Physica D 434, Article ID 133214, 9 p. (2022; Zbl 1498.33016) Full Text: DOI arXiv
van Assche, Walter Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations. (English) Zbl 1443.33028 Foupouagnigni, Mama (ed.) et al., Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser. Tutor. Sch. Workshops Math. Sci., 629-683 (2020). MSC: 33C45 33E17 34M55 60B20 PDFBibTeX XMLCite \textit{W. van Assche}, in: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5--12, 2018. Cham: Birkhäuser. 629--683 (2020; Zbl 1443.33028) Full Text: DOI arXiv
Aptekarev, Alexander I.; van Assche, Walter; Yattselev, Maxim L. Hermite-Padé approximants for a pair of Cauchy transforms with overlapping symmetric supports. (English) Zbl 1362.41001 Commun. Pure Appl. Math. 70, No. 3, 444-510 (2017). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 41A21 30C15 35Q15 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Commun. Pure Appl. Math. 70, No. 3, 444--510 (2017; Zbl 1362.41001) Full Text: DOI arXiv
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter Unique positive solution for an alternative discrete Painlevé I equation. (English) Zbl 1355.39005 J. Difference Equ. Appl. 22, No. 5, 656-675 (2016). Reviewer: Ti-Jun Xiao (Fudan) MSC: 39A12 34M55 39A22 PDFBibTeX XMLCite \textit{P. A. Clarkson} et al., J. Difference Equ. Appl. 22, No. 5, 656--675 (2016; Zbl 1355.39005) Full Text: DOI arXiv Link
Van Assche, Walter; Filipuk, Galina; Zhang, Lun Multiple orthogonal polynomials associated with an exponential cubic weight. (English) Zbl 1309.42037 J. Approx. Theory 190, 1-25 (2015). Reviewer: Pablo Sánchez-Moreno (Granada) MSC: 42C05 PDFBibTeX XMLCite \textit{W. Van Assche} et al., J. Approx. Theory 190, 1--25 (2015; Zbl 1309.42037) Full Text: DOI arXiv
Filipuk, Galina; Van Assche, Walter Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation. (English) Zbl 1269.34095 Proc. Am. Math. Soc. 141, No. 2, 551-562 (2013). Reviewer: Tsvetana Stoyanova (Sofia) MSC: 34M55 33E17 33C47 42C05 PDFBibTeX XMLCite \textit{G. Filipuk} and \textit{W. Van Assche}, Proc. Am. Math. Soc. 141, No. 2, 551--562 (2013; Zbl 1269.34095) Full Text: DOI arXiv
Boelen, Lies; van Assche, Walter Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials. (English) Zbl 1187.39012 Proc. Am. Math. Soc. 138, No. 4, 1317-1331 (2010). MSC: 39A13 33D45 PDFBibTeX XMLCite \textit{L. Boelen} and \textit{W. van Assche}, Proc. Am. Math. Soc. 138, No. 4, 1317--1331 (2010; Zbl 1187.39012) Full Text: DOI
Boelen, Lies; Smet, Christophe; van Assche, Walter \(q\)-discrete Painlevé equations for recurrence coefficients of modified \(q\)-Freud orthogonal polynomials. (English) Zbl 1189.39009 J. Difference Equ. Appl. 16, No. 1, 37-53 (2010). Reviewer: Jacques Sauloy (Toulouse) MSC: 39A13 33C47 33D45 PDFBibTeX XMLCite \textit{L. Boelen} et al., J. Difference Equ. Appl. 16, No. 1, 37--53 (2010; Zbl 1189.39009) Full Text: DOI arXiv
Kuijlaars, A. B. J.; Mclaughlin, K. T.-R.; Van Assche, W.; Vanlessen, M. The Riemann–Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]. (English) Zbl 1082.42017 Adv. Math. 188, No. 2, 337-398 (2004). Reviewer: Doron S. Lubinsky (Atlanta) MSC: 42C05 30E25 33C10 35Q15 PDFBibTeX XMLCite \textit{A. B. J. Kuijlaars} et al., Adv. Math. 188, No. 2, 337--398 (2004; Zbl 1082.42017) Full Text: DOI arXiv
Aptekarev, A. I.; Van Assche, W. Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight. (English) Zbl 1061.30035 J. Approximation Theory 129, No. 2, 129-166 (2004). Reviewer: Arno Kuijlaars (Leuven) MSC: 30E25 30E10 30E15 41A21 41A60 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{W. Van Assche}, J. Approx. Theory 129, No. 2, 129--166 (2004; Zbl 1061.30035) Full Text: DOI