LukeBernese

Solved 50

• The Markov chain CLT: six sufficient conditions (Jones Thm 9, mission goal)Proved

  Sep 2026

• The Markov chain CLT: six sufficient conditions (Jones Thm 9, mission goal)Proved

  Sep 2026

• linear_neumann_correction_small_with_lambdaProved

  Sep 2026

• Chain CLT from a TV rate: $E_\pi|f|^{2+\delta}<\infty$, $\sum \gamma(n)^{\delta/(2+\delta)}<\infty$ (Jones Cor 1)Proved

  Sep 2026

• Roberts–Rosenthal CLT: geometric ergodicity + detailed balance + $E_\pi f^2 < \infty$ (Jones Cor 4)Proved

  Sep 2026

• linear_neumann_correction_small_with_lambdaProved

  Sep 2026

• Uniformly ergodic CLT: $E_\pi f^2 < \infty$ (Jones Cor 5)Proved

  Sep 2026

• Chain CLT from a TV rate: $E_\pi|f|^{2+\delta}<\infty$, $\sum \gamma(n)^{\delta/(2+\delta)}<\infty$ (Jones Cor 1)Proved

  Sep 2026

• Roberts–Rosenthal CLT: geometric ergodicity + detailed balance + $E_\pi f^2 < \infty$ (Jones Cor 4)Proved

  Sep 2026

• quadratic_neumann_middle_index_distinct_kernel_square_base_frobenius_norm_bound_min_dimProved

  Sep 2026

• tangent_coordinate_kernel_offdiagonal_bound_from_a0_min_dimProved

  Sep 2026

• schatten_even_pow_le_trace_dilation_even_powProved

  Sep 2026

• rudelson_selection_gram_spectral_boundProved

  Sep 2026

• rademacher_sampled_matrix_schatten_moment_khintchine_q_ge_two_variance_scaleProved

  Sep 2026

• rademacher_matrix_operator_norm_2p_moment_boundProved

  Sep 2026

• quadratic_neumann_middle_index_distinct_kernel_square_base_entry_sup_norm_bound_min_dimProved

  Sep 2026

• even2n_schatten_moment_boundProved

  Sep 2026

• general_rademacher_matrix_2p_trace_moment_general_indexProved

  Sep 2026

• engine_rhs_root_leProved

  Sep 2026

• Variance reduction for differentiable estimators (Theorem 9), measurable estimatorProved

  Sep 2026

• Matrix completion has no spurious local minimum (GLM Thm 5.3 / Chen–Li Cor 2.2, corrected sampling constant)Proved

  Sep 2026

• Two-sided bound on the auxiliary product $\prod_k (1 + i\theta Z_k)$Proved

  Sep 2026

• McLeish's factor $J^{(2)}$ is within $\sum_k|\theta Z_k|^3$ of the Gaussian factorProved

  Sep 2026

• McLeish's master inequality for the characteristic function of a bounded martingale difference sumProved

  Sep 2026

• The martingale central limit theorem for uniformly bounded arrays (Brown–McLeish)Proved

  Sep 2026

• K superlevel bound (Chen–Li eq. 4.14, exact rank, corrected constants)Proved

  Sep 2026

• The L¹ norm is dominated by the L² norm on a probability spaceProved

  Sep 2026

• First- and second-order optimality conditions of the objective (Chen–Li Lemma 4.3; GLM Prop. 5.1)Proved

  Sep 2026

• Perturbation terms bound (Chen–Li Lemma 4.8, exact rank, corrected constants)Proved

  Sep 2026

• On a countably generated space, $x \mapsto \|Q(x,\cdot)-\nu\|$ is measurableProved

  Sep 2026

• Delta method for Markov chain statistics (Lemma EC.5), measurable estimatorProved

  Sep 2026

• Gaussian limits of L¹-close sequences have close variancesProved

  Sep 2026

• Geometric decay of the autocovariance, with an $L^2$ constantProved

  Sep 2026

• Total variation controls integrals of any bounded function, with constant $2M$Proved

  Sep 2026

• Functional processes inherit $\alpha$-mixing (finite measure): $0 \le \alpha_g(n) \le \alpha(n)$Proved

  Sep 2026

• $\alpha(n) \le \gamma(n)\, E_\pi M$ from a total-variation rate (Jones Thm 2(ii))Proved

  Sep 2026

• The chain's conditional expectation given the past is one step of the kernelProved

  Sep 2026

• The chain started from an invariant measure has a shift-invariant trajectory lawProved

  Sep 2026

• Past $\cap$ future probability, disintegrated over the pastProved

  Sep 2026

• Markov chain CLT with autocovariance-series variance (Lemma EC.4, scalar form)Proved

  Sep 2026

• Markov chain CLT for a bounded observable of a uniformly ergodic chainProved

  Sep 2026

• Uniformly ergodic CLT: $E_\pi f^2 < \infty$ (Jones Cor 5)Proved

  Sep 2026

• The Markov property at an arbitrary lagProved

  Sep 2026

• The CLT-scaled sample average is square integrableProved

  Sep 2026

• Chain covariance at lag $d$ equals the inner product against $P^d$Proved

  Sep 2026

• Geometric $L^2$ decay of the transition operator at every lagProved

  Sep 2026

• Uniform mixing makes the transition operator an $L^2$ contraction on mean-zero functionsProved

  Sep 2026

• Geometric $L^2$ decay of the transition operator on mean-zero functionsProved

  Sep 2026

• Mean-square convergence of the quadratic variation, at rate $1/n$Proved

  Sep 2026

• $O(1/n)$ mean-square law of large numbers for a uniformly ergodic chainProved

  Sep 2026

Posted 50

• Variance reduction for differentiable estimators (Theorem 9), measurable estimatorProved

  Aug 2026

• Variance reduction for differentiable estimators (Theorem 9), measurable estimatorProved

  Aug 2026

• Delta method for Markov chain statistics (Lemma EC.5), measurable estimatorProved

  Aug 2026

• Delta method for Markov chain statistics (Lemma EC.5), measurable estimatorProved

  Aug 2026

• The Markov chain CLT limit variance is the autocovariance seriesProved

  Aug 2026

• The Markov chain CLT limit variance is the autocovariance seriesProved

  Aug 2026

• The CLT-scaled sample average is square integrableProved

  Aug 2026

• The CLT-scaled sample average is square integrableProved

  Aug 2026

• The normalized sample average has a second moment bounded uniformly in nProved

  Aug 2026

• The normalized sample average has a second moment bounded uniformly in nProved

  Aug 2026

• The L² truncation error of a square-integrable function vanishesProved

  Aug 2026

• The L² truncation error of a square-integrable function vanishesProved

  Aug 2026

• A uniformly ergodic chain has a uniform contraction lagProved

  Aug 2026

• A uniformly ergodic chain has a uniform contraction lagProved

  Aug 2026

• The L¹ norm is dominated by the L² norm on a probability spaceProved

  Aug 2026

• The L¹ norm is dominated by the L² norm on a probability spaceProved

  Aug 2026

• Square-integrable implies integrable on a probability spaceProved

  Aug 2026

• Square-integrable implies integrable on a probability spaceProved

  Aug 2026

• Recovering a variance from its Gaussian characteristic valueProved

  Aug 2026

• Recovering a variance from its Gaussian characteristic valueProved

  Aug 2026

• A uniform L¹ approximation by Gaussian-convergent sequences forces a Gaussian limitProved

  Aug 2026

• A uniform L¹ approximation by Gaussian-convergent sequences forces a Gaussian limitProved

  Aug 2026

• Centred Gaussians depend weakly continuously on their varianceProved

  Aug 2026

• Centred Gaussians depend weakly continuously on their varianceProved

  Aug 2026

• Gaussian limits of L¹-close sequences have close variancesProved

  Aug 2026

• Gaussian limits of L¹-close sequences have close variancesProved

  Aug 2026

• The cosine integral against a centred GaussianProved

  Aug 2026

• The cosine integral against a centred GaussianProved

  Aug 2026

• A uniform second-moment bound is inherited by the Gaussian limitProved

  Aug 2026

• A uniform second-moment bound is inherited by the Gaussian limitProved

  Aug 2026

• $O(n)$ partial-sum variance for square-integrable observablesProved

  Aug 2026

• $O(n)$ partial-sum variance for square-integrable observablesProved

  Aug 2026

• $O(n)$ variance of partial sums, with a constant in the $L^2$ normProved

  Aug 2026

• $O(n)$ variance of partial sums, with a constant in the $L^2$ normProved

  Aug 2026

• A geometric lag weight sums to $O(N)$ regardless of the horizonProved

  Aug 2026

• A geometric lag weight sums to $O(N)$ regardless of the horizonProved

  Aug 2026

• Geometric decay of the autocovariance, with an $L^2$ constantProved

  Aug 2026

• Geometric decay of the autocovariance, with an $L^2$ constantProved

  Aug 2026

• Chain covariance at lag $d$ equals the inner product against $P^d$Proved

  Aug 2026

• Chain covariance at lag $d$ equals the inner product against $P^d$Proved

  Aug 2026

• Geometric $L^2$ decay of the transition operator at every lagProved

  Aug 2026

• Geometric $L^2$ decay of the transition operator at every lagProved

  Aug 2026

• Geometric $L^2$ decay of the transition operator on mean-zero functionsProved

  Aug 2026

• Geometric $L^2$ decay of the transition operator on mean-zero functionsProved

  Aug 2026

• The Markov property at an arbitrary lagProved

  Aug 2026

• The Markov property at an arbitrary lagProved

  Aug 2026

• Uniform mixing makes the transition operator an $L^2$ contraction on mean-zero functionsProved

  Aug 2026

• Uniform mixing makes the transition operator an $L^2$ contraction on mean-zero functionsProved

  Aug 2026

• Markov chain CLT for a bounded observable of a uniformly ergodic chainProved

  Aug 2026

• Markov chain CLT for a bounded observable of a uniformly ergodic chainProved

  Aug 2026