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Charlier, ChristopheORCID iD iconorcid.org/0000-0001-6890-344x
Publications (10 of 29) Show all publications
Charlier, C. & Lenells, J. (2024). Boussinesq's equation for water waves: Asymptotics in Sector I. Advances in Nonlinear Analysis, 13(1), Article ID 20240022.
Open this publication in new window or tab >>Boussinesq's equation for water waves: Asymptotics in Sector I
2024 (English)In: Advances in Nonlinear Analysis, ISSN 2191-9496, Vol. 13, no 1, article id 20240022Article in journal (Refereed) Published
Abstract [en]

In a recent study, we showed that the large ( x , t ) \left(x,t) behavior of a class of physically relevant solutions of Boussinesq's equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the positive x x -axis, referred to as Sector I, we stated without proof an exact expression for the leading asymptotic term together with an error estimate. Here, we provide a proof of this asymptotic formula.

Place, publisher, year, edition, pages
Walter de Gruyter GmbH, 2024
Keywords
asymptotics, Boussinesq equation, Riemann-Hilbert problem, initial value problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-350112 (URN)10.1515/anona-2024-0022 (DOI)001253434300001 ()2-s2.0-85198451295 (Scopus ID)
Note

QC 20240708

Available from: 2024-07-08 Created: 2024-07-08 Last updated: 2024-07-24Bibliographically approved
Charlier, C. & Lenells, J. (2024). Boussinesq’s Equation for Water Waves: Asymptotics in Sector V. SIAM Journal on Mathematical Analysis, 56(3)
Open this publication in new window or tab >>Boussinesq’s Equation for Water Waves: Asymptotics in Sector V
2024 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 56, no 3Article in journal (Refereed) Published
Abstract [en]

We consider the Boussinesq equation on the line for a broad class of Schwartz initialdata for which (i) no solitons are present, (ii) the spectral functions have generic behavior near\pm 1,and (iii) the solution exists globally. In a recent work, we identified 10 main sectors describing theasymptotic behavior of the solution, and for each of these sectors we gave an exact expression for theleading asymptotic term. In this paper, we give a proof for the formula corresponding to the sectorxt\in (0,1\surd 3)

Place, publisher, year, edition, pages
Society for Industrial & Applied Mathematics (SIAM), 2024
Keywords
Boussinesq equation, long-time asymptotics, Riemann--Hilbert problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-350116 (URN)10.1137/23M1587671 (DOI)001248211500007 ()2-s2.0-85190821361 (Scopus ID)
Note

QC 20240708

Available from: 2024-07-08 Created: 2024-07-08 Last updated: 2024-07-08Bibliographically approved
Blackstone, E., Charlier, C. & Lenells, J. (2024). Toeplitz determinants with a one-cut regular potential and Fisher-Hartwig singularities I. Equilibrium measure supported on the unit circle. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 154(5), 1431-1472
Open this publication in new window or tab >>Toeplitz determinants with a one-cut regular potential and Fisher-Hartwig singularities I. Equilibrium measure supported on the unit circle
2024 (English)In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 154, no 5, p. 1431-1472Article in journal (Refereed) Published
Abstract [en]

We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential, (ii) Fisher-Hartwig singularities and (iii) a smooth function in the background. The potential is associated with an equilibrium measure that is assumed to be supported on the whole unit circle. For constant potentials, the equilibrium measure is the uniform measure on the unit circle and our formulas reduce to well-known results for Toeplitz determinants with Fisher-Hartwig singularities. For non-constant, our results appear to be new even in the case of no Fisher-Hartwig singularities. As applications of our results, we derive various statistical properties of a determinantal point process which generalizes the circular unitary ensemble.

Place, publisher, year, edition, pages
Cambridge University Press, 2024
Keywords
asymptotics, Fisher-Hartwig singularities, Riemann-Hilbert problems, Toeplitz determinants
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-348020 (URN)10.1017/prm.2023.73 (DOI)001333588900009 ()2-s2.0-85168996023 (Scopus ID)
Note

QC 20240705

Available from: 2024-07-05 Created: 2024-07-05 Last updated: 2025-03-21Bibliographically approved
Charlier, C. & Moreillon, P. (2023). ON THE GENERATING FUNCTION OF THE PEARCEY PROCESS. The Annals of Applied Probability, 33(4), 3240-3277
Open this publication in new window or tab >>ON THE GENERATING FUNCTION OF THE PEARCEY PROCESS
2023 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 33, no 4, p. 3240-3277Article in journal (Refereed) Published
Abstract [en]

The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number m of intervals. We derive an integral representation for it in terms of a Hamiltonian that is related to a system of 6m + 2 coupled nonlinear equations. We also obtain asymptotics for the generating function as the size of the intervals get large, up to and including the constant term. This work generalizes some results of Dai, Xu, and Zhang, which correspond to m = 1.

Place, publisher, year, edition, pages
Institute of Mathematical Statistics, 2023
Keywords
Pearcey point process, generating function asymptotics, Hamiltonian, Riemann-Hilbert problems
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-333738 (URN)10.1214/22-AAP1890 (DOI)001031710500020 ()2-s2.0-85166146889 (Scopus ID)
Note

QC 20230810

Available from: 2023-08-10 Created: 2023-08-10 Last updated: 2023-08-10Bibliographically approved
Blackstone, E., Charlier, C. & Lenells, J. (2023). The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem. Communications on Pure and Applied Mathematics, 76(11), 3300-3345
Open this publication in new window or tab >>The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem
2023 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 76, no 11, p. 3300-3345Article in journal (Refereed) Published
Abstract [en]

The Bessel process models the local eigenvalue statistics near 0 of certain large positive definite matrices. In this work, we consider the probability (Figure presented.) where (Figure presented.) and (Figure presented.) is any non-negative integer. We obtain asymptotics for this probability as the size of the intervals becomes large, up to and including the oscillations of order 1. In these asymptotics, the most intricate term is a one-dimensional integral along a linear flow on a g-dimensional torus, whose integrand involves ratios of Riemann θ-functions associated to a genus g Riemann surface. We simplify this integral in two generic cases: (a) If the flow is ergodic, we compute the leading term in the asymptotics of this integral explicitly using Birkhoff's ergodic theorem. (b) If the linear flow has certain “good Diophantine properties”, we obtain improved estimates on the error term in the asymptotics of this integral. In the case when the flow is both ergodic and has “good Diophantine properties” (which is always the case for (Figure presented.), and “almost always” the case for (Figure presented.)), these results can be combined, yielding particularly precise and explicit large gap asymptotics.

Place, publisher, year, edition, pages
Wiley, 2023
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-338562 (URN)10.1002/cpa.22119 (DOI)001020331500001 ()2-s2.0-85162854828 (Scopus ID)
Note

QC 20231107

Available from: 2023-11-07 Created: 2023-11-07 Last updated: 2023-11-07Bibliographically approved
Charlier, C., Lenells, J. & Wang, D. S. (2023). The “good” boussinesq equation: long-time asymptotics. Analysis & PDE, 16(6), 1351-1388
Open this publication in new window or tab >>The “good” boussinesq equation: long-time asymptotics
2023 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 16, no 6, p. 1351-1388Article in journal (Refereed) Published
Abstract [en]

We consider the initial-value problem for the “good” Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a 3×3-matrix Riemann–Hilbert problem. We establish formulas for the long-time asymptotics of the solution by performing a Deift–Zhou steepest descent analysis of a regularized version of this Riemann–Hilbert problem. Our results are valid for generic solitonless Schwartz class solutions whose space-average remains bounded as t→∞.

Place, publisher, year, edition, pages
Mathematical Sciences Publishers, 2023
Keywords
asymptotics, Boussinesq equation, initial value problem, inverse scattering transform, Riemann–Hilbert problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-337444 (URN)10.2140/apde.2023.16.1351 (DOI)001077068600002 ()2-s2.0-85171468984 (Scopus ID)
Note

QC 20231024

Available from: 2023-10-06 Created: 2023-10-06 Last updated: 2023-10-24Bibliographically approved
Charlier, C. & Lenells, J. (2023). The hard-to-soft edge transition: Exponential moments, central limit theorems and rigidity. Journal of Approximation Theory, 285, Article ID 105833.
Open this publication in new window or tab >>The hard-to-soft edge transition: Exponential moments, central limit theorems and rigidity
2023 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 285, article id 105833Article in journal (Refereed) Published
Abstract [en]

The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter alpha. For this point process, we obtain (1) exponential moment asymptotics, up to and including the constant term, (2) asymptotics for the expectation and variance of the counting function, (3) several central limit theorems and (4) a global rigidity upper bound.

Place, publisher, year, edition, pages
Elsevier BV, 2023
Keywords
Exponential moments, Bessel point process, Random matrix theory, Asymptotic analysis, Rigidity, Riemann-Hilbert problems, Airy point process
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-324869 (URN)10.1016/j.jat.2022.105833 (DOI)000934830700004 ()2-s2.0-85141326835 (Scopus ID)
Note

QC 20230320

Available from: 2023-03-20 Created: 2023-03-20 Last updated: 2023-03-20Bibliographically approved
Charlier, C. (2022). Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities. Selecta Mathematica, New Series, 28(3), Article ID 50.
Open this publication in new window or tab >>Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities
2022 (English)In: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 28, no 3, article id 50Article in journal (Refereed) Published
Abstract [en]

Muttalib-Borodin determinants are generalizations of Hankel determinants and depend on a parameter theta > 0. In this paper, we obtain large n asymptotics for nxn Muttalib-Borodin determinants whose weight possesses an arbitrary number of Fisher-Hartwig singularities. As a corollary, we obtain asymptotics for the expectation and variance of the real and imaginary parts of the logarithm of the underlying characteristic polynomial, several central limit theorems, and some global bulk rigidity upper bounds. Our results are valid for all theta > 0.

Place, publisher, year, edition, pages
Springer Nature, 2022
Keywords
Muttalib-Borodin ensembles, Fisher-Hartwig singularities, Rigidity
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-310256 (URN)10.1007/s00029-022-00762-6 (DOI)000766173300001 ()2-s2.0-85126177274 (Scopus ID)
Note

QC 20220325

Available from: 2022-03-25 Created: 2022-03-25 Last updated: 2022-06-25Bibliographically approved
Blackstone, E., Charlier, C. & Lenells, J. (2022). Gap probabilities in the bulk of the Airy process. Random Matrices. Theory and Applications, 11(02), Article ID 2250022.
Open this publication in new window or tab >>Gap probabilities in the bulk of the Airy process
2022 (English)In: Random Matrices. Theory and Applications, ISSN 2010-3263, Vol. 11, no 02, article id 2250022Article in journal (Refereed) Published
Abstract [en]

We consider the probability that no points lie on g large intervals in the bulk of the Airy point process. We make a conjecture for all the terms in the asymptotics up to and including the oscillations of order 1, and we prove this conjecture for g = 1.

Place, publisher, year, edition, pages
World Scientific Pub Co Pte Ltd, 2022
Keywords
Large gap probability, Airy point process, random matrix theory, Riemann-Hilbert problem
National Category
Mathematical Analysis Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-312182 (URN)10.1142/S2010326322500228 (DOI)000789116800001 ()2-s2.0-85116915606 (Scopus ID)
Note

QC 20220518

Available from: 2022-05-18 Created: 2022-05-18 Last updated: 2022-06-25Bibliographically approved
Blackstone, E., Charlier, C. & Lenells, J. (2022). Oscillatory Asymptotics for the Airy Kernel Determinant on Two Intervals. International mathematics research notices, 2022(4), 2636-2687, Article ID rnaa205.
Open this publication in new window or tab >>Oscillatory Asymptotics for the Airy Kernel Determinant on Two Intervals
2022 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2022, no 4, p. 2636-2687, article id rnaa205Article in journal (Refereed) Published
Abstract [en]

We obtain asymptotics for the Airy kernel Fredholm determinant on two intervals. We give explicit formulas for all the terms up to and including the oscillations of order 1, which are expressed in terms of Jacobi theta-functions.

Place, publisher, year, edition, pages
Oxford University Press (OUP), 2022
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-309784 (URN)10.1093/imrn/rnaa205 (DOI)000754760500008 ()2-s2.0-85125482904 (Scopus ID)
Note

QC 20220314

Available from: 2022-03-14 Created: 2022-03-14 Last updated: 2022-06-25Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0001-6890-344x

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