| 1. |
- Blackstone, Elliot, et al.
(author)
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Gap probabilities in the bulk of the Airy process
- 2022
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In: Random Matrices. Theory and Applications. - : World Scientific Pub Co Pte Ltd. - 2010-3263. ; 11:02
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Journal article (peer-reviewed)abstract
- 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.
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| 2. |
- Blackstone, Elliot, et al.
(author)
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Oscillatory Asymptotics for the Airy Kernel Determinant on Two Intervals
- 2022
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In: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 2022:4, s. 2636-2687
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Journal article (peer-reviewed)abstract
- 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.
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| 3. |
- Charlier, Christophe
(author)
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Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities
- 2022
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In: Selecta Mathematica, New Series. - : Springer Nature. - 1022-1824 .- 1420-9020. ; 28:3
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Journal article (peer-reviewed)abstract
- 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.
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| 4. |
- Charlier, Christophe, et al.
(author)
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The "Good" Boussinesq Equation : a Riemann-Hilbert Approach
- 2022
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In: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518 .- 1943-5258. ; 71:4, s. 1505-1562
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Journal article (peer-reviewed)abstract
- We develop an inverse scattering transform formalism for the "good " Boussinesq equation on the line. Assuming that the solution exists, we show that it can be expressed in terms of the solution of a 3 x 3 matrix Riemann-Hilbert problem. The Riemann-Hilbert problem is formulated in terms of two reflection coefficients whose definitions involve only the initial data, and it has a form which makes it suitable for the evaluation of long-time asymptotics via Deift-Zhou steepest descent arguments.
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| 5. |
- Çlnar, Mustafa Neşet, et al.
(author)
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Toward Optimized Charge Transport in Multilayer Reduced Graphene Oxides
- 2022
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In: Nano Letters. - : American Chemical Society (ACS). - 1530-6992 .- 1530-6984. ; 22:6, s. 2202-2208
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Journal article (peer-reviewed)abstract
- In the context of graphene-based composite applications, a complete understanding of charge conduction in multilayer reduced graphene oxides (rGO) is highly desirable. However, these rGO compounds are characterized by multiple and different sources of disorder depending on the chemical method used for their synthesis. Most importantly, the precise role of interlayer interaction in promoting or jeopardizing electronic flow remains unclear. Here, thanks to the development of a multiscale computational approach combining first-principles calculations with large-scale transport simulations, the transport scaling laws in multilayer rGO are unraveled, explaining why diffusion worsens with increasing film thickness. In contrast, contacted films are found to exhibit an opposite trend when the mean free path becomes shorter than the channel length, since conduction becomes predominantly driven by interlayer hopping. These predictions are favorably compared with experimental data and open a road toward the optimization of graphene-based composites with improved electrical conduction.
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