We design randomized approximation schemes for the partition function of antiferromagnetic Ising models with uniform external field on random regular bipartite graphs. Our algorithm generalizes the approach of Kocurek, Oveis Gharan and Tjowasi (arXiv, 2026) for hard-core models on the same random graph model beyond the uniqueness threshold. We show that, as long as $\lambda$ is upper bounded by a constant and $\lambda(1 - \beta) \lesssim \Delta^{-1/2}$, an efficient randomized algorithm approximates the partition function with high probability. The algorithm first truncates configurations that are large on either side of the bipartition and then samples from Gibbs distributions conditioned on fixed sizes on one or both sides. To choose an optimal truncation bound, we establish concentration properties of the Gibbs distribution on random regular bipartite graphs. Then we apply high-dimensional expansion and prove trickle-down theorems to obtain fast samplers for the conditioned distributions.
In this paper, we derive quenched scaling limits for linear functionals and the empirical spin field of Ising models on inhomogeneous random graphs generated by a graphon (encompassing both dense and sparse graphs), in the high-temperature regime. We first prove a joint central limit theorem (CLT) for finite collection...
These results establish a direct and quantitative link between random matrix disorder on graphs and the performance of continuous-time quantum walk search, and suggest that disorder, rather than being merely an obstacle, can be exploited as a tunable parameter in quantum search protocols.
Sabyasachi Chakraborty, T. Čadež, Sonjoy Majumder et al.· 0 citations
We determine the critical probability for Bernoulli bond percolation on essentially any finite graph. Namely, letting $\lambda(G)$ denote the spectral radius (maximum eigenvalue) of $G$, we prove that the critical probability is at $1/\lambda(G)$: above this probability there is typically a component of order $\Omega(\...
Mixing time bounds for Markov chains play a central role in characterizing the sample complexity of learning and inference from correlated data. While the mixing behavior of symmetric random walks on standard graph structures such as cycles, tori, and hypercubes is well understood, the impact of transition asymmetry re...
Mrudula A Mahindrakar, Hrushikesh A Kant, Avhishek Chatterjee· International Conference on...· 0 citations
The main idea is to introduce a family of quadratic tilts in the left-right occupation imbalance and show that each tilted measure can be sampled efficiently using Glauber dynamics, and obtain efficient approximate counting and sampling at every fugacity $\lambda>0$ whenever.
The Watts-Strogatz random graph model on $n$ vertices with parameters $K$ (a positive even integer) and $p \in [0, 1]$ is constructed in two steps. First, one starts with a ring lattice on $n$ vertices, where each vertex is connected to its $K/2$ nearest neighbors on each side. Each edge in turn is then independently r...
Grégoire Meunier, Sean O’Rourke· 0 citations
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