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• W2963002110 abstract "We study a random system of cn linear equations over n variables in GF(2), where each equation contains exactly r variables; this is equivalent to r-XORSAT. Previous work has established a clustering threshold, c^*_r for this model: if c=c_r^*-epsilon for any constant epsilon>0 then with high probability all solutions form a well-connected cluster; whereas if c=c^*_r+epsilon, then with high probability the solutions partition into well-connected, well-separated clusters (with probability tending to 1 as n goes to infinity). This is part of a general clustering phenomenon which is hypothesized to arise in most of the commonly studied models of random constraint satisfaction problems, via sophisticated but mostly non-rigorous techniques from statistical physics. We extend that study to the range c=c^*_r+o(1), and prove that the connectivity parameters of the r-XORSAT clusters undergo a smooth transition around the clustering threshold." @default.
• W2963002110 created "2019-07-30" @default.
• W2963002110 creator A5072889645 @default.
• W2963002110 creator A5083257155 @default.
• W2963002110 date "2017-11-20" @default.
• W2963002110 modified "2023-09-24" @default.
• W2963002110 title "Inside the clustering window for random linear equations" @default.
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• W2963002110 doi "https://doi.org/10.1002/rsa.20740" @default.
• W2963002110 hasPublicationYear "2017" @default.
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