## 168 Citations

A large deviation principle for the Erdős–Rényi uniform random graph

- Mathematics
- 2018

Starting with the large deviation principle (ldp) for the Erdős–Rényi binomial random graph G(n, p) (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the ldp for the…

Moderate deviations of subgraph counts in the Erdős-Rényi random graphs 𝐺(𝑛,𝑚) and 𝐺(𝑛,𝑝)

- MathematicsTransactions of the American Mathematical Society
- 2020

The main contribution of this article is an asymptotic expression for the rate associated with moderate deviations of subgraph counts in the Erdős-Rényi random graph
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m
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G(n,m)…

Sparse random graphs with many triangles

- Computer Science, Mathematics
- 2021

This paper derives asymptotically sharp bounds on the probability that the Erdős-Rényi random graph contains a large number of vertices that are part of a triangle, and shows that, conditionally on this event, with high probability the graph contains an almost complete subgraph, i.e., the triangles form a near-clique, and has the same local limit as the original Erd� Hungarian random graph.

Large Deviation Principle for the Maximal Eigenvalue of Inhomogeneous Erdős-Rényi Random Graphs

- MathematicsJournal of Theoretical Probability
- 2021

We consider an inhomogeneous Erdős-Rényi random graph GN with vertex set [N ] = {1, . . . , N} for which the pair of vertices i, j ∈ [N ], i 6= j, is connected by an edge with probability r( i N , j…

Large Deviations for Dense Random Graphs

- Mathematics
- 2017

A dense graph is a graph whose number of edges is comparable to the square of the number of vertices. The main result of this chapter is the formulation and proof of the large deviation principle for…

The upper tail problem for induced 4-cycles in sparse random graphs

- Mathematics
- 2022

Building on the techniques from the breakthrough paper of Harel, Mousset and Samotij, which solved the upper tail problem for cliques, we compute the asymptotics of the upper tail for the number of…

SPECTRAL EDGE IN SPARSE RANDOM GRAPHS: UPPER AND LOWER TAIL LARGE DEVIATIONS BY BHASWAR

- Mathematics
- 2020

In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erdős-Rényi random graph Gn,p, in the regime of p where the edge of…

The Large Deviation Principle for Interacting Dynamical Systems on Random Graphs

- Mathematics, Computer ScienceCommunications in Mathematical Physics
- 2022

The LDP for random graphs is translated to a class of interacting dynamical systems on such graphs and it is demonstrated that the solutions of the dynamical models depend continuously on the underlying graphs with respect to the cut-norm and apply the contraction principle.

Large deviation for the empirical degree distribution of an Erdos-Renyi graph

- Mathematics
- 2013

With $(d_1,\cdots,d_n)$ denoting the labeled degrees of an Erdos Renyi graph with parameter $\beta/n$, the large deviation principle for $\frac{1}{n}\sum\limits_{j=1}^n\delta_{d_j}$ (the empirical…

## References

SHOWING 1-10 OF 27 REFERENCES

The missing log in large deviations for triangle counts

- Computer Science, MathematicsRandom Struct. Algorithms
- 2012

This paper solves the problem of sharp large deviation estimates for the upper tail of the number of triangles in an Erdős‐Rényi random graph, by establishing a logarithmic factor in the exponent…

Graph limits and exchangeable random graphs

- Computer Science
- 2007

A clear connection between deFinetti's theorem for exchangeable arrays and the emerging area of graph limits is developed and the graph theory is translated into more classical prob- ability.

Metrics for sparse graphs

- Mathematics, Computer Science
- 2007

This paper deals mainly with graphs with $o(n^2)$ but $\omega(n)$ edges: a companion paper [arXiv:0812.2656] will discuss the (more problematic still) case of {\em extremely sparse} graphs, with O( n) edges.

Applications of Stein's method for concentration inequalities

- Mathematics
- 2010

Stein’s method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this…

Random graphs with a given degree sequence

- Mathematics
- 2011

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is…

Testing properties of graphs and functions

- Mathematics
- 2008

We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the…

Szemerédi’s Lemma for the Analyst

- Mathematics
- 2007

Abstract.Szemerédi’s regularity lemma is a fundamental tool in graph theory: it has many applications to extremal graph theory, graph property testing, combinatorial number theory, etc. The goal of…

Combinatorics, complexity, and chance : a tribute to Dominic Welsh

- Mathematics
- 2007

Preface 1. Orbit counting and the Tutte polynomial 2. Eulerian and bipartite orientable matroids 3. Tutte-Whitney polynomials: some history and generalisations 4. A survey on the use of Markov chains…