In high-dimensional critical percolation the rescaled k-point connection probability converges to an explicit constant, confirming the Aizenman-Newman conjecture.
Preprint: 2510.21595
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A partial reversal of the Simon-Lieb inequality is shown for high-dimensional percolation, implying uniform boundedness of phi_pc(S) and several critical estimates.
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Convergence of $k$-point functions in high dimensional percolation
In high-dimensional critical percolation the rescaled k-point connection probability converges to an explicit constant, confirming the Aizenman-Newman conjecture.
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On reversing the Simon-Lieb inequality in high-dimensional percolation
A partial reversal of the Simon-Lieb inequality is shown for high-dimensional percolation, implying uniform boundedness of phi_pc(S) and several critical estimates.