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.
citing papers explorer
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Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopes
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.
-
Non-colliding space-time inhomogeneous Markov chains
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.
-
Stable size-biasing and the positive scale-mixture order of generalized Gaussian laws
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.
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Temporal Conductance and Bounds on the Voter Model for Dynamic Networks
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.
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Consensus Time in 3-Majority and 2-Choices Is Determined by the Maximum Initial Opinion Density
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.
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Downward conditional monotonicity gives survival and extinction for contact processes in random environments
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.
-
Bayesian Global Fr\'echet Regression via Weak Conditional Expectations
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.
-
Improved Survival Results for the One-Dimensional Renewal Contact Process
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.
-
Error Bounds for Importance Sampling with Estimated Proposal Distributions
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.
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Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
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.
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Asymptotic Replacement for Quantum Channel Products with Applications to Inhomogeneous Matrix Product States
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.
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Atypical Decay Rates for Atypical Heights in Random Recursive Trees
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.
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Best of both worlds: Stochastic & adversarial best-arm identification
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.
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D-MODD: A Diffusion Model of Opinion Dynamics Derived from Online Data
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.
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Mean-Field Analysis of Latent Variable Process Models on Dynamically Evolving Graphs with Feedback Effects
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.
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Cutoff for mixtures of permuted Markov chains: reversible case
Proves cutoff at entropic time log n/h for reversible mixtures of permuted Markov chains under mild assumptions on the base chains.
-
Simultaneous EF1 and approximate MMS allocations for submodular valuations
Existence of EF1 and constant-ρ MMS allocations proven for submodular valuations.
-
Optimal constants of smoothing estimates for quantum harmonic oscillators
Establishes optimal constants and extremizers for smoothing estimates of quantum harmonic oscillators as direct analogues of prior free-particle results.
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Skewed weak and Pareto-tailed strong interactions accompany community diversity and complexity
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.
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Symmetry-Breaking and Hysteresis in a Duplex Voter Model
A duplex voter model on multiplex networks exhibits spontaneous symmetry-breaking and a cusp bifurcation with noise that unfolds explosive versus non-explosive transitions.
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Clipped Gradient Methods for Nonsmooth Convex Optimization under Heavy-Tailed Noise: A Refined Analysis
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.
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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.
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An iterated $I$-projection procedure for solving the generalized minimum information checkerboard copula problem
An iterated I-projection procedure solves the generalized minimum information checkerboard copula problem with convergence guarantees and numerical tests up to dimension four.
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The mean field stubborn voter model
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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Matrix Approximation of Bachelier Option Prices and Greeks under Stochastic Volatility models
A matrix approximation technique computes Bachelier option prices and Greeks under stochastic volatility models for infinitely many strikes from finite expectations.
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Lipschitz stable sequence classes: an approach to Rademacher type and cotype of Lipschitz functions
Introduces Lipschitz stable sequence classes to define (Z,Y)-summing Lipschitz functions and identifies Rademacher type and cotype for Lipschitz functions with these spaces, proving the type case forms a Banach Lipschitz ideal while the cotype does not.
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How long should a block be?
Excessively long blocks lower asymptotic relative efficiency in the block-maxima method, and new likelihood and diagnostic procedures are proposed to check whether a chosen length is adequate under rounding or censoring.
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Adaptive Pricing in Insurance: Generalized Linear Models and Gaussian Process Regression Approaches
Adaptive GLM with MQLE and GP regression with UCB for dynamic insurance pricing, showing parameter convergence and regret analysis under delayed claims.
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Time-dependent structural equation modeling of fans' football fever using activity tracking data during the 2025 DFB Cup final
Football fever in spectators follows a V-shaped time course captured as a latent process from heart rate and stress data via time-dependent structural equation modeling.
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Measuring Stereotype and Deviation Biases in Large Language Models
Four advanced LLMs display significant stereotype bias and deviation bias when generating profiles tied to political affiliation, religion, and sexual orientation.
- Escaping Chaos in Random Multiplicative Functions