Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Rahman, Mustazee"'
Autor:
Rahman, Mustazee, Virag, Balint
A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reconstructed from the shapes of its semi-infinite geodesics. In order to
Externí odkaz:
http://arxiv.org/abs/2410.19070
Autor:
Rahman, Mustazee
Brownian last passage percolation is a classical model of integrable probability and the KPZ universality class. We consider the Brownian last passage model with a functional initial condition: $$BLPP(X;(t,m)) = \max_{0 \leq t_0 \leq t_1 \leq \cdots
Externí odkaz:
http://arxiv.org/abs/2409.19319
Autor:
Rahman, Mustazee, Virag, Balint
We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish their uniqueness and coalescence, and define Busemann functions. We t
Externí odkaz:
http://arxiv.org/abs/2112.06849
Autor:
Johansson, Kurt, Rahman, Mustazee
Publikováno v:
Ann. Probab. 50 no. 2 (2022), 559-590
This article studies the inhomogeneous geometric polynuclear growth model, the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions, focusing on the
Externí odkaz:
http://arxiv.org/abs/2010.07357
Autor:
Johansson, Kurt, Rahman, Mustazee
Publikováno v:
Comm. Pure Appl. Math. 74 (2021), 2561-2627
We study the multi-time distribution in a discrete polynuclear growth model or, equivalently, in directed last-passage percolation with geometric weights. A formula for the joint multi-time distribution function is derived in the discrete setting. It
Externí odkaz:
http://arxiv.org/abs/1906.01053
Autor:
Huang, Brice, Rahman, Mustazee
Publikováno v:
European J. Combin. 81 (2019) 378-393
In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose $G_1, G_2, G_3, \ldots$ is a sequence of finite and connected graphs that share a common universal cover $T$ and such that the proport
Externí odkaz:
http://arxiv.org/abs/1807.06034
Autor:
Quastel, Jeremy, Rahman, Mustazee
Publikováno v:
Annales Henri Lebesgue, volume 3 (2020), pp. 999-1021
We consider the totally asymmetric simple exclusion process with \emph{soft-shock} initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial configuration i
Externí odkaz:
http://arxiv.org/abs/1801.06143
Publikováno v:
Annals of Probability 2019, Vol. 47, No. 3, 1587-1618
We show that in random $K$-uniform hypergraphs of constant average degree, for even $K \geq 4$, local algorithms defined as factors of i.i.d. can not find nearly maximal cuts, when the average degree is sufficiently large. These algorithms have been
Externí odkaz:
http://arxiv.org/abs/1707.05386
Autor:
Gorin, Vadim, Rahman, Mustazee
Publikováno v:
Probability Theory and Related Fields 175 (2019), 45-96
This paper finds the bulk local limit of the swap process of uniformly random sorting networks. The limit object is defined through a deterministic procedure, a local version of the Edelman-Greene algorithm, applied to a two dimensional determinantal
Externí odkaz:
http://arxiv.org/abs/1702.07895
Autor:
Rahman, Mustazee, Virag, Balint
We prove that the random empirical measure of appropriately rescaled particle trajectories of the interchange process on path graphs converges weakly to the deterministic measure of stationary Brownian motion on the unit interval. This is a law of la
Externí odkaz:
http://arxiv.org/abs/1609.07745