The large deviation principle for the Erdős-Rényi random graph
نویسندگان
چکیده
منابع مشابه
First Passage Percolation on the Erdős-Rényi Random Graph
In this paper we explore first passage percolation (FPP) on the Erdős-Rényi random graph Gn(pn), where each edge is given an independent exponential edge weight with rate 1. In the sparse regime, i.e., when npn → λ > 1, we find refined asymptotics both for the minimal weight of the path between uniformly chosen vertices in the giant component, as well as for the hopcount (i.e., the number of ed...
متن کاملExplosive Percolation in Erdős-Rényi-Like Random Graph Processes
The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erdős-Rényi process (ER). It is well known that this process undergoes a phase transition at n/2 edges when, asymptotically almost surely, a linear-sized component appears. Moreover, this phase transition is continuous, i.e., in the limit the function f(c) denoting...
متن کاملA Large Deviation Principle for Random Upper Semicontinuous Functions
We obtain necessary and sufficient conditions in the Large Deviation Principle for random upper semicontinuous functions on a separable Banach space. The main tool is the recent work of Arcones on the LDP for empirical processes.
متن کاملLarge Deviation Principle for Non-Interacting Boson Random Point Processes
Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare these results with those for the case of the normal phase.
متن کاملErdős - Rényi Random Graphs + Forest Fires = Self - Organized Criticality
We modify the usual Erd˝ os-Rényi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent critical state. The authors thank the anonymous referee for thoroughly reading the manuscript. Her/his comments and suggestions hel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2011
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.03.014