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Brownian structure in the KPZ fixed point

- Jacob Calvert, A. Hammond, M. Hegde
- Mathematics
- 2 December 2019

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 in… Expand

Critical point for infinite cycles in a random loop model on trees

- A. Hammond, M. Hegde
- MathematicsThe Annals of Applied Probability
- 30 May 2018

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 and… Expand

Exceptional times when the KPZ fixed point violates Johansson's conjecture on maximizer uniqueness

- Ivan Corwin, A. Hammond, M. Hegde, K. Matetski
- Mathematics
- 11 January 2021

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 later… Expand

Lower deviations in β-ensembles and law of iterated logarithm in last passage percolation

- Riddhipratim Basu, S. Ganguly, M. Hegde, Manjunath Krishnapur
- Mathematics
- 3 September 2019

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 of… Expand

Interlacing and Scaling Exponents for the Geodesic Watermelon in Last Passage Percolation

- Riddhipratim Basu, S. Ganguly, A. Hammond, M. Hegde
- MathematicsCommunications in Mathematical Physics
- 20 June 2020

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 given… Expand

Local and global comparisons of the Airy difference profile to Brownian local time

- S. Ganguly, M. Hegde
- Mathematics
- 22 March 2021

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… Expand

Optimal tail exponents in general last passage percolation via bootstrapping & geodesic geometry

- S. Ganguly, M. Hegde
- Mathematics
- 7 July 2020

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, an… Expand