O. Alekseev

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20232026

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math-ph2026

Local Rank-One Logarithmic Instability for the Mixed Hessian of the Dispersionless Toda $τ$ -Function

Oleg Alekseev

We study a weighted renormalization of the mixed Hessian of the dispersionless Toda $τ$ -function associated with polynomial conformal maps. The starting point is an explicit logari…

math-ph2026

Spectral Structure of the Mixed Hessian of the Dispersionless Toda $τ$ -Function

Oleg Alekseev

We study the mixed Hessian of the dispersionless Toda $τ$ -function for the one-harmonic $s$ -fold symmetric conformal map $f (w) = r w + a w^{1 - s}$ . This Hessian is the susceptibility matr…

math-ph2023

Universality of stochastic Laplacian growth

Oleg Alekseev

We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domai…

Local Rank-One Logarithmic Instability for the Mixed Hessian of the Dispersionless Toda τ-Function

Spectral Structure of the Mixed Hessian of the Dispersionless Toda τ-Function

Universality of stochastic Laplacian growth

Local Rank-One Logarithmic Instability for the Mixed Hessian of the Dispersionless Toda $τ$ -Function

Spectral Structure of the Mixed Hessian of the Dispersionless Toda $τ$ -Function