The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf–Cole transform of the equation. We revisit some monotonicity results as well as the deriva...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2025-06-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.747/ |
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| author | Mazari-Fouquer, Idriss |
| author_facet | Mazari-Fouquer, Idriss |
| author_sort | Mazari-Fouquer, Idriss |
| collection | DOAJ |
| description | The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf–Cole transform of the equation. We revisit some monotonicity results as well as the derivation of several scaling limits by means of the Donsker–Varadhan formula, and we point out several differences between the case of quadratic Hamiltonians and non-quadratic ones. |
| format | Article |
| id | doaj-art-58b4ab96ede0423dadf86b304d05f41d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-58b4ab96ede0423dadf86b304d05f41d2025-08-20T03:58:13ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692025-06-01363G767769310.5802/crmath.74710.5802/crmath.747Mazari-Fouquer, Idriss0CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Université PSL, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, FranceThe goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf–Cole transform of the equation. We revisit some monotonicity results as well as the derivation of several scaling limits by means of the Donsker–Varadhan formula, and we point out several differences between the case of quadratic Hamiltonians and non-quadratic ones.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.747/Effective Hamiltonianprincipal eigenvaluespectral optimisation |
| spellingShingle | Mazari-Fouquer, Idriss Comptes Rendus. Mathématique Effective Hamiltonian principal eigenvalue spectral optimisation |
| topic | Effective Hamiltonian principal eigenvalue spectral optimisation |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.747/ |