11 papers
Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation
Yucheng Liu, Gordon Slade
The study of the Ornstein--Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossove…
Decay of connection probability in high-dimensional continuum percolation
Matthew Dickson, Yucheng Liu
We study a percolation model on called the random connection model. For large, we use the lace expansion to prove that the critical two-point connection probabili…
Universal finite-size scaling in high-dimensional critical phenomena
Yucheng Liu, Jiwoon Park, Gordon Slade
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our…
High-dimensional long-range statistical mechanical models have random walk correlation functions
Yucheng Liu
We consider long-range percolation, Ising model, and self-avoiding walk on , with couplings decaying like where , above the upper critica…
Constructing stable Hilbert bundles via Diophantine approximation
Yucheng Liu, Biao Ma
On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian--Einstein metrics. Our main constructive step is by investigating the…
A general approach to massive upper bound for two-point function with application to self-avoiding walk torus plateau
Yucheng Liu
We prove a sufficient condition for the two-point function of a statistical mechanical model on , , to be bounded uniformly near a critical point by $|x|^{-(d-…