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On Reverse Hypercontractivity
We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev
Testing independence and goodness-of-fit in linear models
This work considers a linear regression model and proposes an omnibus test to simultaneously check the assumption of independence between the error and predictor variables and the goodness-of-fit of the parametric model, and develops distribution theory for the proposed test statistic, under both the null and the alternative hypotheses.
Stochastic population growth in spatially heterogeneous environments
The results provide fundamental insights into “ideal free” movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology.
Parisi Formula, Disorder Chaos and Fluctuation for the Ground State Energy in the Spherical Mixed p-Spin Models
We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for
Phase transitions in the frustrated Ising model on the square lattice
We consider the thermal phase transition from a paramagnetic to stripe-antiferromagnetic phase in the frustrated two-dimensional square-lattice Ising model with competing interactions J1 0 (second
Another look at the moment method for large dimensional random matrices
The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the  well known moment method which invokes the trace formula. Its success has been
Ashkin-teller criticality and pseudo-first-order behavior in a frustrated Ising model on the square lattice.
We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J(1) < 0 (nearest-neighbor, ferromagnetic) and J(2) > 0 (second-neighbor,
Duality between the deconfined quantum-critical point and the bosonic topological transition
Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden
Spectra of Large Random Trees
We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a
Coulomb phase diagnostics as a function of temperature, interaction range, and disorder.
The detailed shape of pinch points can be used to read off the relative sizes of entropic and magnetic Coulomb interactions of monopoles in spin ice, and the question of why pinch points have been experimentally observed for Ho(1.7)Y(0.3)Ti(2)O(7) even at high temperature in the presence of strong disorder is resolved.