For large beta the TW density takes the form exp(-beta Phi(a)) with Phi(a) obtained as the solution of a Painleve II equation via saddle-point analysis of the stochastic Airy operator.
Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
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abstract
We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the Kardar-Parisi-Zhang theory in 1+1 dimensions. Moreover, we reveal that the distribution and the two-point correlation of the interface fluctuations are universal ones governed by the largest eigenvalue of random matrices. This provides quantitative experimental evidence of the universality prescribing detailed information of scale-invariant fluctuations.
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cond-mat.stat-mech 1years
2025 1verdicts
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The Tracy-Widom distribution at large Dyson index
For large beta the TW density takes the form exp(-beta Phi(a)) with Phi(a) obtained as the solution of a Painleve II equation via saddle-point analysis of the stochastic Airy operator.