Regularized last-iterate solvers select the maximum-entropy Nash equilibrium while regret-averaging methods select lower-entropy faces on zero-sum Nash polytopes, verified on analytic testbeds and a 180-game ensemble.
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Freedman, Another note on the borel-cantelli lemma and the strong law, with the poisson approxi- mation as a by-product, Annals of Probability 1 (6) (1973) 910–925
31 Pith papers cite this work. Polarity classification is still indexing.
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Derives leading asymptotics for collision-time tails of integrable inhomogeneous Markov chains via steepest-descent analysis and Karlin-McGregor expansion, confirming a prediction for push-block particle systems.
Generalized Gaussians satisfy X_p =^d V X_q with positive V independent of X_q if and only if p ≤ q, with explicit V constructed from α-stable laws and size-biasing when p < q.
Defines temporal conductance Φ for dynamic networks and proves the voter model consensus time is O(m/(d_min Φ)) with a tight lower bound.
Consensus time in 3-Majority is ilde{\Theta}(\min\{1/\|\alpha^{(0)}\|_\infty, \sqrt{n}\}) and in 2-Choices is \tilde{\Theta}(1/\|\alpha^{(0)}\|_\infty) w.h.p., governed by maximum initial opinion density for every starting configuration.
Introduces downward conditional monotonicity for MMPP to obtain stochastic domination bounds that determine survival and extinction regimes for contact processes in finite-state random environments via QBD eigenvalue comparison.
A Bayesian global Fréchet regression method is introduced via a Fréchet Bayes rule that reduces the problem to scalar tasks, allows prior-data interpolation, and remains valid under moment conditions using weak conditional expectations.
Proves finiteness of λ_c(μ) for the 1D renewal contact process when interarrival distributions are arithmetic or have uniformly small atomic components on short intervals.
Derives non-asymptotic error bounds for standard, defensive, and self-normalized importance sampling with random KDE proposals from geometrically ergodic Markov chains, separating n^{-1/2} Monte Carlo error from MIAE/MISE proposal error.
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
Products of finite-dimensional quantum channels asymptotically forget input states under decay of the centered trace-Dobrushin coefficient, yielding unique replacement channels and convergence for deterministic and random inhomogeneous MPS.
Random recursive trees exhibit polynomial upper-tail and stretched-exponential lower-tail large deviation probabilities for height, with an atypical prefactor in the lower tail that grows slower than any n-fold iterated logarithm.
No algorithm can be optimal in both stochastic and adversarial best-arm identification; a new parameter-free algorithm matches the derived lower bound up to log factors in stochastic cases while handling adversarial rewards.
D-MODD is a data-derived Langevin stochastic differential equation whose transition kernel reproduces the one-step opinion change probabilities observed in social media data on a polarized climate topic.
Characterizes the distributional mean-field limit of co-evolving latent space networks with feedback, including empirical measures and graphon convergence, via a conditional propagation of chaos result.
Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
Existence of EF1 and constant-ρ MMS allocations proven for submodular valuations.
Establishes optimal constants and extremizers for smoothing estimates of quantum harmonic oscillators as direct analogues of prior free-particle results.
Empirical plant-animal network data and generalized Lotka-Volterra simulations identify SWAPS interaction distributions as a community signature that requires taxonomic constraints, multiple interaction types, and accompanies elevated diversity and complexity.
A duplex voter model on multiplex networks exhibits spontaneous symmetry-breaking and a cusp bifurcation with noise that unfolds explosive versus non-explosive transitions.
Refined analysis of Clipped SGD yields improved high-probability rates involving generalized effective dimension and establishes matching lower bounds showing optimality for convergence in expectation under heavy-tailed noise.
Dynamic state expansion with infection memory improves pair approximation accuracy for SIS epidemic threshold and quasi-stationary distribution on arbitrary networks.
An iterated I-projection procedure solves the generalized minimum information checkerboard copula problem with convergence guarantees and numerical tests up to dimension four.
Derives novel scaling limit and explicit consensus probabilities for mean-field voter model with heavy-tailed waiting times, governed by extreme-value landscape of the tail index.
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Threshold and quasi-stationary distribution for the SIS model on networks
Dynamic state expansion with infection memory improves pair approximation accuracy for SIS epidemic threshold and quasi-stationary distribution on arbitrary networks.