Related papers: Stochastic version of the Erdos-Renyi limit theore…
We study a generalization of the Random Energy Model to the case when the number of exponential factors varies at random. Also a relation between REM and the Erd"os-R'enyi limit theorem for maximums of partial sums is considered.
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and…
Erdos-Renyi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdos-Renyi type limit laws for Holder observables on dynamical systems modeled by…
We prove entropic and total variation versions of the Erd\H{o}s-Kac limit theorem for the maximum of the partial sums of i.i.d. random variables with densities.
The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
We get central limit type theorems for the total number of edges in the generalized random graphs with random vertex weights under different moment conditions on distributions of the weights.
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
We derive the limiting distribution for the largest eigenvalues of the adjacency matrix for a stochastic blockmodel graph when the number of vertices tends to infinity. We show that, in the limit, these eigenvalues are jointly multivariate…
Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We…
We prove that the generalized Randic index over graphs following the Erd\H{o}s-Renyi model, for both the sparse and dense regimes, is concentrated around its mean when the number of vertices tends to infinity.
In this paper we define a directed percolation over Erdos-Renyi graphs and derive weak limit results for the resulting stochastic process.
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…
We identify the scaling limit of random intersection graphs inside their critical windows. The limit graphs vary according to the clustering regimes, and coincide with the continuum Erdos--Renyi graph in two out of the three regimes. Our…