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Soft edge results for longest increasing paths on the planar lattice

   
@article{ECP1519,
	author = {Nicos Georgiou},
	title = {Soft edge results for longest increasing paths on the planar lattice},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {15},
	year = {2010},
	keywords = {Bernoulli matching model; Discrete TASEP; soft edge; weak law of large numbers; last passage model; increasing paths},
	abstract = {For two-dimensional last-passage time models of weakly increasing paths, interesting scaling limits have been proved for points close the axis (the hard edge). For strictly increasing paths of Bernoulli($p$) marked sites, the relevant boundary is the line $y=px$. We call this the soft edge to contrast it with the hard edge. We prove laws of large numbers for the maximal cardinality of a strictly increasing path in the rectangle $[p^{-1}n -xn^a]\times[n]$ as the parameters $a$ and $x$ vary.  The results change qualitatively as $a$ passes through the value $1/2$.},
	pages = {no. 1, 1-13},
	issn = {1083-589X},
	doi = {10.1214/ECP.v15-1519},    
        url = {http://ecp.ejpecp.org/article/view/1519}}