Abstract
The integral over twon ×n hermitan matricesZ(g, c)=∫dAdBexp{−tr[A 2+B 2−2cAB+g/n(A 4+B 4)]} is evaluated in the limit of largen. For this purpose use is made of the theory of diffusion equation and that of orthogonal polynomials with a non-local weight. The above integral arises in the study of the planar approximation to quantum field theory.
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Brezin, E., Itzykson, C., Parisi, G., Zuber, J. B.: Commun. Math. Phys.59, 35–51 (1978)
Bessis, D.: A new method in the combinatoric of the topological expansion, Commun. Math. Phys.69, 147–163 (1979)
Itzykson, C., Zuber, J. B.: The planar approximation (II), J. Math. Phys.21, 411–421 (1980)
Mehta, M. L.: Random matrices. Chap. 3. New York: Academic Press 1967
Morse, P. M.: Feshbach, H.: Methods of mathematical physics. Chap. 2.4. New York: McGraw-Hill 1953
Hardy, G. H., Littlewood, J. E., Polya, G.: Inequalities. p. 138. Cambridge: University Press 1964
Chadha S., Mahoux G., Metha M. L.: A Method of integration over Matrix variables. II. J. Phys. A (in press)
Bessis D., Itzykson C., Zuber J. B., Adv. Appl. Math.1, 109–157 (1980)
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Communicated by E. Brézin
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Mehta, M.L. A method of integration over matrix variables. Commun.Math. Phys. 79, 327–340 (1981). https://doi.org/10.1007/BF01208498
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DOI: https://doi.org/10.1007/BF01208498