We compute Stokes matrices for generalised Airy equations and prove that they are regular unipotent (up to multiplication with the formal monodromy). This class of differential was defined by Katz includes classical equation. In addition, it which not rigid. Our approach is based on topological computation enhanced Fourier-Sato transform a perverse sheaf due D'Agnolo, Hien, Morando Sabbah.

We study the model of totally asymmetric exclusion process with generalized update, which compared to usual process, has an additional parameter enhancing clustering particles. derive exact multiparticle distributions distances travelled by particles on infinite lattice for two types initial conditions: step and alternating ones. Two different scaling limits formulas are studied. Under first as...

The localization of fluorescent microspheres is often employed for drift correction and image registration in single molecule microscopy, and is commonly carried out by fitting a point spread function to the image of the given microsphere. The mismatch between the point spread function and the image of the microsphere, however, calls into question the suitability of this localization approach. ...

We present a class of diffraction-free partially coherent beams each member which is comprised finite power, non-accelerating Airy bump residing on statistically homogeneous, Gaussian-correlated background. examine free-space propagation soft apertured realizations the proposed and show that their evolution governed by two spatial scales: coherence width background aperture size. A relative mag...

We construct a class of ℓ $\ell$ -adic local systems on A 1 $\mathbb {A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These are finite field analogues generalizations classical equation y ′ ( z ) = $y^{\prime \prime }(z)=zy(z)$ . employ geometric Langlands correspondence sought-after as eigenvalues certain rigid Hecke eigensheaves, following methods developed Hei...

We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to nonuniversal and trivial extended processes.