Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA large deviation principle for block models
175
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study upper tail large deviations for homomorphism densities of regular graphs. We identify the existence of a symmetric phase, where the graph, conditioned on the rare event, looks like a block model with the same block sizes as the generating graphon. In specific examples, we also identify the existence of a symmetry breaking regime, where the conditional structure is not a block model with compatible dimensions. This identifies a reentrant phase transition phenomenon for this problem---analogous to one established for Erdos-Renyi random graphs (Chatterjee-Dey(2010), Chatterjee-Varadhan(2011)). Finally, extending the analysis of Lubetzky-Zhao(2015), we identify the precise boundary between the symmetry and symmetry breaking regime for homomorphism densities of regular graphs and the operator norm on Erdos-Renyi bipartite graphs.
rate research
Read More
Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007.14508] proved a large deviation principle for block model random graphs with rational block ratios. We strengthen their result by allowing any block ratios (and also establish a simpler formula for the rate function). We apply the new result to derive a large deviation principle for graph sampling from any given step graphon.
In this article, we develop a framework to study the large deviation principle for matrix models and their quantiz
This paper is devoted to investigating the Freidlin-Wentzells large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence criteria to prove the Laplace principle for McKean-Vlasov type SPDEs, which is equivalent to the large deviation principle. Moreover, we do not assume any compactness condition of embedding in the Gelfand triple to handle both the cases of bounded and unbounded domains in applications. The main results can be applied to various McKean-Vlasov type SPDEs such as distribution dependent stochastic porous media type equations and stochastic p-Laplace type equations.
We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute explicit limiting logarithmic moment generating functions for both the classical and the invariant models. The shape function of this model exhibits a flat edge in certain directions, and we also discuss the rate function and limiting log-moment generating functions in those directions.
We consider a dynamic ErdH{o}s-Renyi random graph (ERRG) on $n$ vertices in which each edge switches on at rate $lambda$ and switches off at rate $mu$, independently of other edges. The focus is on the analysis of the evolution of the associated empirical graphon in the limit as $ntoinfty$. Our main result is a large deviation principle (LDP) for the sample path of the empirical graphon observed until a fixed time horizon. The rate is $binom{n}{2}$, the rate function is a specific action integral on the space of graphon trajectories. We apply the LDP to identify (i) the most likely path that starting from a constant graphon creates a graphon with an atypically large density of $d$-regular subgraphs, and (ii) the mostly likely path between two given graphons. It turns out that bifurcations may occur in the solutions of associated variational problems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
