In the subcritical regime m = m_c(1-ε) with ε→0 and ε³n→∞, the largest component L1 satisfies L1 = (1+o_p(1)) * [2(α+2)/(α+1)] ε^{-2} log(ε³ n) for fixed α>0 (and analogous limits when α(n)→a).
Reflected solutions of backward SDE's, and related obstacle problems for PDE's
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No universal constant exists allowing convex-hull bounds with controlled L_log norms for the difference set of arbitrary finite T under symmetric Weibull(r) processes when 0<r<1.
Proves Poisson-Dirichlet edge statistics for full Gibbs ensembles on random lattices and quenched thermal concentration with visibility curve c=γ^{-2} for primitive directions.
Necessary and sufficient conditions are given for convergence to a unique IPVT on proper pointed measured metric spaces, with proofs for higher-rank symmetric spaces and Diestel-Leader graphs showing parameter independence and distinguishable cells.
Newton's recursive mixture estimator is a discrete gradient flow on the Fisher-Rao manifold of probability measures.
Proves sharp Gaussian isoperimetric inequality for conjugate heat-kernel measures along Ricci flow via monotonicity formula, with consequences for concentration estimates, log-Sobolev inequalities, and related results.
Uniform analyticity of local observables is proved in FK-percolation under mixing conditions, yielding analyticity of Potts/Ising magnetization in the supercritical regime and susceptibility in the subcritical regime.
Constructs canonical p-energy measures for strongly local p-energy forms, proves chain/Leibniz rules and uniqueness, and shows coincidence with Korevaar-Schoen-type measures via a p-analogue of Le Jan's domination principle.
Proves O(1/sqrt(penalty)) convergence rate between reflected quadratic-generator BSDEs and penalized BSDEs via BMO martingales, with application to Euler polygonal approximation for sub-quadratic generators.
The paper establishes existence and uniqueness for generalized mean-reflected McKean-Vlasov BSDEs via stability estimates for uniqueness and a penalization-plus-smooth-approximation argument for existence.
Bayesian nonparametric mixtures of Poisson and normal regressions using DP and PY priors are fitted via MCMC to predict claims frequency and severity, with an illustration on French motor insurance data.
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