Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2FCZ______%3A_____%2F24%3AN0000098" target="_blank" >RIV/CZ______:_____/24:N0000098 - isvavai.cz</a>
Result on the web
<a href="https://iopscience.iop.org/article/10.1088/1751-8121/ad1e1a" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/ad1e1a</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ad1e1a" target="_blank" >10.1088/1751-8121/ad1e1a</a>

Result language
angličtina
Original language name
Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices
Original language description
We evaluate, in the large-N limit, the complete probability distribution P(A,m) of the values A of the sum & sum;(N)(i=1)|lambda(i)|(m), where lambda(i) (i=1,2,& mldr;,N) are the eigenvalues of a Gaussian random matrix, and m is a positive real number. Combining the Coulomb gas method with numerical simulations using a matrix variant of the Wang-Landau algorithm, we found that, in the limit of N ->infinity, the rate function of P(A,m) exhibits phase transitions of different characters. The phase diagram of the system on the (A,m) plane is surprisingly rich, as it includes three regions: (i) a region with a single-interval support of the optimal spectrum of eigenvalues, (ii) a region emerging for m<2 where the optimal spectrum splits into two separate intervals, and (iii) a region emerging for m>2 where the maximum or minimum eigenvalue ``evaporates" from the rest of eigenvalues and dominates the statistics of A. The phase transition between regions (i) and (iii) is of second order. Analytical arguments and numerical simulations strongly suggest that the phase transition between regions (i) and (ii) is of (in general) fractional order p=1+1/|m-1|, where 02 occur at the ground state of the Coulomb gas which corresponds to the Wigner's semicircular distribution.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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