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- W2972253721 abstract "Consider the upper tail probability that the homomorphism count of a fixed graph $H$ within a large sparse random graph $G_n$ exceeds its expected value by a fixed factor $1+delta$. Going beyond the Erdős-Renyi model, we establish here explicit, sharp upper tail decay rates for sparse random $d_n$-regular graphs (provided $H$ has a regular $2$-core), and for sparse uniform random graphs. We further deal with joint upper tail probabilities for homomorphism counts of multiple graphs $H_1,ldots, H_k$ (extending the known results for $k=1$), and for inhomogeneous graph ensembles (such as the stochastic block model), we bound the upper tail probability by a variational problem analogous to the one that determines its decay rate in the case of sparse Erdős-Renyi graphs." @default.
- W2972253721 created "2019-09-12" @default.
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- W2972253721 date "2019-09-06" @default.
- W2972253721 modified "2023-09-28" @default.
- W2972253721 title "Upper Tail For Homomorphism Counts In Constrained Sparse Random Graphs" @default.
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