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• W2021252979 abstract "Consider a continuous time random walk in $mathbb{Z}$ with independent and exponentially distributed jumps $pm1$. The model in this paper consists in an infinite number of such random walks starting from the complement of ${-m,-m+1,ldots,m-1,m}$ at time -t, returning to the same starting positions at time t, and conditioned not to intersect. This yields a determinantal process, whose gap probabilities are given by the Fredholm determinant of a kernel. Thus this model consists of two groups of random walks, which are contained within two ellipses which, with the choice $msimeq2t$ to leading order, just touch: so we have a tacnode. We determine the new limit extended kernel under the scaling $m=lfloor2t+sigma t^{1/3}rfloor$, where parameter $sigma$ controls the strength of interaction between the two groups of random walkers." @default.
• W2021252979 created "2016-06-24" @default.
• W2021252979 creator A5046754172 @default.
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• W2021252979 date "2013-07-01" @default.
• W2021252979 modified "2023-10-18" @default.
• W2021252979 title "Nonintersecting random walks in the neighborhood of a symmetric tacnode" @default.
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• W2021252979 doi "https://doi.org/10.1214/11-aop726" @default.
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