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<p>We obtain new lower bounds on the critical points for various models of oriented percolation. The method relies on establishing a stochastic domination of the percolation processes by multitype Galton-Watson trees. This approach can be applied to classical bond and site oriented percolation on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3466_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>, as well as to other lattices, such as inhomogeneous ones, and in three dimensions.</p>

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An Update on Lower Bounds for the Critical Values of Oriented Percolation Models

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Olivier Couronné

摘要

We obtain new lower bounds on the critical points for various models of oriented percolation. The method relies on establishing a stochastic domination of the percolation processes by multitype Galton-Watson trees. This approach can be applied to classical bond and site oriented percolation on \(\mathbb {Z}^2\) Z 2 , as well as to other lattices, such as inhomogeneous ones, and in three dimensions.