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SUMMARY:Functional Central Limit Theorems for Inhomogeneous Random Graphs
DTSTART:20260114T150000
DTEND:20260114T154000
DTSTAMP:20260415T111759Z
UID:0ae9cf77c9ae27e27477879c5ec839b4e3863e58e7e6c4c621302a21
CATEGORIES:Conferences - Seminars
DESCRIPTION:Akshay Sakanaveeti\nInhomogeneous random graphs (IRGs) are gen
 eralisations of the Erdos-Renyi random graph. Several random graph models 
 can be viewed as inhomogeneous random graphs with an appropriate type spac
 e. Although tools to understand the law of large numbers limits and phase
  transitions are well established\, there has been little progress on cent
 ral limit theorems for IRGs. The main reason for this is that combinatoria
 l techniques\, which are the primary tools used for Erdős–Rényi random
  graphs\, fail in this setting. In this work\, we study the dynamic versi
 on of IRG and establish \n\n	Functional central limit theorems for the in
 finite vector of microscopic type-densities and characterizations of the l
 imits as infinite-dimensional Gaussian processes in a certain Banach space
  in both subcritical and supercritical regimes.\n	Functional (joint) centr
 al limit theorems for macroscopic observables of the giant component in th
 e supercritical regime\, including size\, surplus\, and its type composit
 ion. \n	Leveraging these results\, we also establish the central limit th
 eorem for the weight of the minimum spanning tree with iid Exponential edg
 e weights on dense graph sequences driven by an underlying finite type gra
 phon. \n
LOCATION:https://epfl.zoom.us/j/64196363217?pwd=zvKsGLaeYhiD99JUue52eGV463
 ZX2e.1
STATUS:CONFIRMED
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