Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Sen, Sanchayan"'
We develop a general universality technique for establishing metric scaling limits of critical random discrete structures exhibiting mean-field behavior that requires four ingredients: (i) from the barely subcritical regime to the critical window, co
Externí odkaz:
http://arxiv.org/abs/2303.10082
Autor:
Bhamidi, Shankar, Sen, Sanchayan
A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade [31,32,38,70] is as follows: f
Externí odkaz:
http://arxiv.org/abs/2009.10696
We establish the global lower mass-bound property for the largest connected components in the critical window for the configuration model when the degree distribution has an infinite third moment. The scaling limit of the critical percolation cluster
Externí odkaz:
http://arxiv.org/abs/2005.02566
Autor:
Miermont, Grégory, Sen, Sanchayan
We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum random tree
Externí odkaz:
http://arxiv.org/abs/1908.04403
Autor:
Addario-Berry, Louigi, Sen, Sanchayan
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and so far the
Externí odkaz:
http://arxiv.org/abs/1810.03802
We study the fixation time of the identity of the leader, i.e., the most massive component, in the general setting of Aldous's multiplicative coalescent [4, 5], which in an asymptotic sense describes the evolution of the component sizes of a wide arr
Externí odkaz:
http://arxiv.org/abs/1703.09908
Publikováno v:
Electron. J. Probab. 25, no. 47, 1-57 (2020)
We study limits of the largest connected components (viewed as metric spaces) obtained by critical percolation on uniformly chosen graphs and configuration models with heavy-tailed degrees. For rank-one inhomogeneous random graphs, such results were
Externí odkaz:
http://arxiv.org/abs/1703.07145
Publikováno v:
Ann. Inst. H. Poincar\'e Probab. Statist., 56, no. 3 (2020), 1515-1558
We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with exponent $\tau-1$, where $\tau\in (3,4)$. The component sizes
Externí odkaz:
http://arxiv.org/abs/1612.00650
Autor:
Bhamidi, Shankar, Sen, Sanchayan
We provide an explicit algorithm for sampling a uniform simple connected random graph with a given degree sequence. By products of this central result include: (i) continuum scaling limits of uniform simple connected graphs with given degree sequence
Externí odkaz:
http://arxiv.org/abs/1608.07153
Publikováno v:
Electron.J.Probab. 22 (2017) 1-33
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the asymptotic
Externí odkaz:
http://arxiv.org/abs/1605.02868