Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952702249> ?p ?o ?g. }
- W2952702249 abstract "The eigenvalue statistics of a pair $(M_1,M_2)$ of $ntimes n$ Hermitian matrices taken random with respect to the measure $$frac{1}{Z_n}expbig(-nTr (V(M_1)+W(M_2)-tau M_1M_2)big) {rm d}M_1 {rm d} M_2 $$ can be described in terms of two families of biorthogonal polynomials. In this paper we give a steepest descent analysis of a $4 times 4$ matrix-valued Riemann-Hilbert problem characterizing one of the families of biorthogonal polynomials in the special case $W(y)=y^4/4$ and $V$ an even polynomial. As a result we obtain the limiting behavior of the correlation kernel associated to the eigenvalues of $M_1$ (when averaged over $M_2$) in the global and local regime as $nto infty$ in the one-cut regular case. A special feature in the analysis is the introduction of a vector equilibrium problem involving both an external field and an upper constraint." @default.
- W2952702249 created "2019-06-27" @default.
- W2952702249 creator A5044081911 @default.
- W2952702249 creator A5074892626 @default.
- W2952702249 date "2008-07-30" @default.
- W2952702249 modified "2023-09-27" @default.
- W2952702249 title "Universality in the two matrix model: a Riemann-Hilbert steepest descent analysis" @default.
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