Periodic TASEP and a Cylindrical dual-RSK
We introduce a version of RSK that captures the dynamics of periodic TASEP. This work is building towards a cylindrical analogue of (AB Dieker, J Warren, 2008).
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arXiv subjects
Tomas Kojar
Publications and source records attributed to Tomas Kojar.
Decoupling and Multipoint moments for the Inverse of the Gaussian multiplicative chaos
In this article we study the decoupling structure and multipoint moment of the inverse of the Gaussian multiplicative chaos. It is also the second part of preliminary work for extending the work in "Random conformal weldings" (by K. Astala, P. Jones, A. Kupiainen, E. Saksman) to the existence of Lehto welding for the inverse. In particular, we prove that the dilatation of the inverse homeomorphism on the positive real line is in $L^{1}([0,1]\times[0,2])$.
math.PR↗
Inverse of the Gaussian multiplicative chaos: Lehto welding of Independent Quantum disks
In this article, we use the framework of "Random conformal weldings" (by K. Astala, P. Jones, A. Kupiainen, E. Saksman) to prove the existence of Lehto-welding for the inverse for $\gamma<0.1818$ and independent copies for $\gamma_{2}\leq\gamma_{1}<0.1818$. In particular, we obtain the existence of some conformaly invariant loop $\Gamma$ that glues two disks with boundary length given by independent copies of GMC on the unit circle. It is still unclear how to show that those loops $\Gamma$ are in fact SLE-loops in a parallel proof to "Integrability of SLE via conformal welding of random surfaces" (by Morris Ang, Nina Holden, and Xin Sun).
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Inverse of the Gaussian multiplicative chaos: an integration by parts formula
In this article, we study the analogue of the integration by parts formula from "Hitting times for Gaussian processes" in the context of GMC and its inverse.
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Inverse of the Gaussian multiplicative chaos: Moments
In this article we systematically study the general properties and the single-point moments of the inverse of the Gaussian multiplicative chaos.
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A Left passage explorer model
This is a short note describing a model generalizing the Harmonic explorer [6] that might be of interest and it is $\textit{not}$ intended for publication in a journal. The conjectured continuous model should have the same left-passage probability as SLE_$k$ but possibly be a different curve.
math.PR↗
Brownian motion and Symmetrization
In this survey we explore the salient connections made between Brownian motion, symmetrization and complex analysis in the last 60 years starting with Kakutani's paper (1944) equating harmonic measure and exit probability. To exemplify these connections we will survey the techniques used in the literature to prove isoperimetric results for exit probabilities and Riesz capacities.
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