allychan327

Solved 50

• Theorem 13.1 -- spectral gap from contracting couplingsProved

  Aug 2026

• Lemma 12.1 -- basic spectral facts for stochastic matricesProved

  Aug 2026

• Section 9.1 -- the network walk is reversibleProved

  Aug 2026

• Proposition 6.10 -- the strong stationary time boundProved

  Aug 2026

• Lemma 6.13 -- total variation is bounded by separationProved

  Aug 2026

• Section 7.1.1 -- the counting boundProved

  Aug 2026

• Section 7.1.2 -- the diameter boundProved

  Aug 2026

• Lemma 7.9 -- projections do not increase total variationProved

  Aug 2026

• Section 4.5 -- standard mixing-time inequalitiesProved

  Aug 2026

• Theorem 4.9 -- the Convergence TheoremProved

  Aug 2026

• Lemma 4.12 -- submultiplicativity of $\bar d$Proved

  Aug 2026

• Proposition 4.7 -- the coupling characterization of total variationProved

  Aug 2026

• Section 3.3.2 -- stationarity of the Glauber dynamicsProved

  Aug 2026

• Proposition 4.5 -- total variation via bounded test functionsProved

  Aug 2026

• Lemma 4.13 -- a walk and its inverse walk mix at the same rateProved

  Aug 2026

• Lemma 4.11 -- comparing $d(t)$ and $\bar d(t)$Proved

  Aug 2026

• Section 3.2.2 -- the Metropolis-Hastings chain for a general base chainProved

  Aug 2026

• Section 3.2.1 -- the Metropolis chain for a symmetric base chainProved

  Aug 2026

• Proposition 4.2 -- total variation as half the $\ell^1$ distanceProved

  Aug 2026

• Lemma 1.13 -- expected hitting times of an irreducible chain are finiteProved

  Aug 2026

• Corollary 1.17 -- existence and uniqueness of the stationary distributionProved

  Aug 2026

• Proposition 2.13 -- irreducibility of a group walkProved

  Aug 2026

• Proposition 1.7 -- a positive power of an irreducible aperiodic chainProved

  Aug 2026

• Proposition 1.22 -- the time reversal of a chainProved

  Aug 2026

• Lemma 1.6 -- the period is constant on an irreducible chainProved

  Aug 2026

• Corollary 1.17 (uniqueness) -- at most one stationary distributionProved

  Aug 2026

• Lemma 1.16 -- harmonic functions of an irreducible chain are constantProved

  Aug 2026

• Examples 1.12 and 1.20 -- simple random walk on a graphProved

  Aug 2026

• Propositions 2.12 and 2.14 -- random walks on finite groupsProved

  Aug 2026

• Proposition 1.19 -- detailed balance implies stationarityProved

  Aug 2026

• Asymptotically optimal UCB finite-time regret boundProved

  Jul 2026

• UCB suboptimal-arm pull-count tailProved

  Jul 2026

• UCB pull-count ceiling bound (Eq. 7.10)Proved

  Jul 2026

• Marginalized local transitions inherit agent-wise TV boundsProved

  Jul 2026

• Markov entanglement bounds the Q-value decomposition error (Thm. 4)Proved

  Jul 2026

• linear_neumann_off_diagonal_coefficient_bound_from_bernstein_base_bounds_fixProved

  Jun 2026

• linear_neumann_off_diagonal_two_term_bernstein_threshold_absorbed_under_sample_bound_fixProved

  Jun 2026

• variance_le_half_sum_resample_sqProved

  Jun 2026

• variance_le_sum_expected_condVarCoordProved

  Jun 2026

• efron_stein_increment_leProved

  Jun 2026

• variance_partialIntegral_le_integral_varianceProved

  Jun 2026

• condExp_piFinset_eq_marginalProved

  Jun 2026

• condExp_comap_fst_eq_partial_integralProved

  Jun 2026

• variance_partial_integral_leProved

  Jun 2026

• expected_condVar_coord_eq_half_resampleProved

  Jun 2026

• efron_stein_condExp_comap_snd_eq_partial_integralProved

  Jun 2026

• variance_eq_half_resample_difference_piProved

  Jun 2026

• resample_measure_preservingProved

  Jun 2026

• integral_condVar_le_integral_sq_sub_of_strongly_measurableProved

  Jun 2026

• condVar_le_condExp_sq_sub_of_strongly_measurableProved

  Jun 2026

Posted 33

• Algorithm 6 per-arm expected pull-count boundProved

  Jul 2026

• UCB pull-count bad-event inclusionProved

  Jul 2026

• Stopped centered reward stackDefinition

  Jul 2026

• UCB suboptimal-arm good event (Eqs. 7.6–7.10)Proved

  Jul 2026

• Bellman Q-decomposition error from local TV controlProved

  Jul 2026

• Marginalized local transitions inherit agent-wise TV boundsProved

  Jul 2026

• linear_neumann_off_diagonal_coefficient_bound_small_with_lambda_fixOpen

  Jun 2026

• linear_neumann_off_diagonal_coefficient_bound_from_bernstein_base_bounds_fixProved

  Jun 2026

• linear_neumann_off_diagonal_two_term_bernstein_threshold_absorbed_under_sample_bound_fixProved

  Jun 2026

• variance_le_half_sum_resample_sqProved

  Jun 2026

• variance_le_sum_expected_condVarCoordProved

  Jun 2026

• efron_stein_increment_leProved

  Jun 2026

• variance_partialIntegral_le_integral_varianceProved

  Jun 2026

• condExp_piFinset_eq_marginalProved

  Jun 2026

• condExp_comap_fst_eq_partial_integralProved

  Jun 2026

• variance_partial_integral_leProved

  Jun 2026

• expected_condVar_coord_eq_half_resampleProved

  Jun 2026

• efron_stein_condExp_comap_snd_eq_partial_integralProved

  Jun 2026

• variance_eq_half_resample_difference_piProved

  Jun 2026

• resample_measure_preservingProved

  Jun 2026

• integral_condVar_le_integral_sq_sub_of_strongly_measurableProved

  Jun 2026

• condVar_le_condExp_sq_sub_of_strongly_measurableProved

  Jun 2026

• condVar_sub_of_strongly_measurable_eqProved

  Jun 2026

• variance_eq_sum_expected_condVarProved

  Jun 2026

• variance_condExp_telescopeProved

  Jun 2026

• variance_nested_two_stepProved

  Jun 2026

• variance_condExp_le_varianceProved

  Jun 2026

• expected_condVar_le_varianceProved

  Jun 2026

• bernoulli_cube_linear_functional_variance_eqProved

  Jun 2026

• variance_bernoulli_indicator_eqProved

  Jun 2026

• variance_weighted_independent_sum_eqProved

  Jun 2026

• efron_stein_resampling_variance_identityProved

  Jun 2026

• spectral_norm_eq_singular_value_zeroProved

  Jun 2026