6 papers
Free energy of Ising models under a spectral condition
Andrea Montanari, Michael Ren
A sequence of sparse weighted graphs indexed by the number of vertices is said to be left-convergent if all (suitably weighted) subgraph counts converge to a lim…
Stanley-Wilf Limits for Patterns in Rooted Labeled Forests
Michael Ren
Building off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests. We prove a forest analogue of the Stanl…
Locality of critical percolation on expanding graph sequences
Michael Ren, Nike Sun
We study the locality of critical percolation on finite graphs: let be a sequence of finite graphs, converging locally weakly to a (random, rooted) infinite graph . Consid…
Circular Trace Reconstruction
Shyam Narayanan, Michael Ren
Trace reconstruction is the problem of learning an unknown string from independent traces of , where traces are generated by independently deleting each bit of with some…
Wilf Equivalences for Patterns in Rooted Labeled Forests
Michael Ren
Building off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests, resolving some of their conjectures and…
Quasi-Invariants in Characteristic and Twisted Quasi-Invariants
Michael Ren, Xiaomeng Xu
The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 were…