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Brownian structure in the KPZ fixed point
Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed inExpand
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Optimal tail exponents in general last passage percolation via bootstrapping & geodesic geometry
We consider last passage percolation on $\mathbb Z^2$ with general weight distributions, which is expected to be a member of the Kardar-Parisi-Zhang (KPZ) universality class. In this model, anExpand
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Lower Deviations in $\beta$-ensembles and Law of Iterated Logarithm in Last Passage Percolation
For the last passage percolation (LPP) on $\mathbb{Z}^2$ with exponential passage times, let $T_{n}$ denote the passage time from $(1,1)$ to $(n,n)$. We investigate the law of iterated logarithm ofExpand
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Interlacing and scaling exponents for the geodesic watermelon in last passage percolation
In discrete planar last passage percolation (LPP), random values are assigned independently to each vertex in $\mathbb Z^2$, and each finite upright path in $\mathbb Z^2$ is ascribed the weight givenExpand
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Exceptional times when the KPZ fixed point violates Johansson's conjecture on maximizer uniqueness
In 2002, Johansson conjectured that the maximum of the Airy2 process minus the parabola x is almost surely achieved at a unique location [Joh03, Conjecture 1.5]. This result was proved a decade laterExpand
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Local and global comparisons of the Airy difference profile to Brownian local time
There has recently been much activity within the Kardar-Parisi-Zhang universality class spurred by the construction of the canonical limiting object, the parabolic Airy sheet S : R → R [DOV18]. TheExpand
Critical point for infinite cycles in a random loop model on trees
We study a spatial model of random permutations on trees with a time parameter $T>0$, a special case of which is the random stirring process. The model on trees was first analysed by Bj\"ornberg andExpand
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