Shuze Chen

Solved 50

• Online Load Balancing on Unrelated MachinesProved

  Aug 2026

• A Full Feasible Dual Prevents Algorithmic FailureProved

  Aug 2026

• Restricting the Full Dual Witness to a PrefixProved

  Aug 2026

• Explicit Prefix Load Bound for Unrelated-Machine SchedulingProved

  Aug 2026

• Maintained Prefix Primal FeasibilityProved

  Aug 2026

• Exact Primal Accounting IdentityProved

  Aug 2026

• Weak Duality for Finite Standard-Form Linear ProgramsProved

  Aug 2026

• Barrier method: $O(\sqrt{m}\log(1/\varepsilon))$ Newton stepsProved

  Aug 2026

• Newton complexity for self-concordant functionsProved

  Aug 2026

• Barrier method $O(\sqrt m)$ Newton complexityDisproved

  Aug 2026

• Newton complexity for self-concordant functionsDisproved

  Aug 2026

• Newton-decrement contraction of the pure stepProved

  Aug 2026

• Uniform layer-cake grid sums recover weighted lower integralsProved

  Aug 2026

• Suboptimality from the Newton decrementProved

  Aug 2026

• Löwner–John rounding for polytopesProved

  Aug 2026

• KKT identities at the normalized optimumProved

  Aug 2026

• Strict LMI theorem of alternativesProved

  Aug 2026

• Generalized hinging-hyperplane representation of CPWL functionsProved

  Aug 2026

• Finite affine maxima reduce to $(n+1)$-argument hingesProved

  Aug 2026

• Uniqueness of the Löwner–John ellipsoidProved

  Aug 2026

• Existence of the Löwner–John ellipsoidProved

  Aug 2026

• Nonstrict LMI theorem of alternativesProved

  Aug 2026

• SDP strong dualityProved

  Aug 2026

• Per-centering potential gapProved

  Aug 2026

• Trust-region strong duality (level-set form)Proved

  Aug 2026

• Dines's theorem: vector witness for PSD averages of two quadratic formsProved

  Aug 2026

• The affine log barrier is self-concordantProved

  Aug 2026

• The S-procedure (losslessness)Proved

  Aug 2026

• Gradient descent with backtracking: linear rateProved

  Aug 2026

• Concavity of $\log\det$Proved

  Aug 2026

• Fenchel–Moreau biconjugationProved

  Aug 2026

• Second-order characterization of convexityProved

  Aug 2026

• Double dual cone = closed conic hullProved

  Aug 2026

• Deterministic sampling-deviation bound $|D_{\Omega,t}(AC^\top,BD^\top)|\le\|\Omega-tJ\|\cdot(\text{row factors})$ (Chen–Li Lemma 4.4)Proved

  Aug 2026

• Existence of an aligned exact factor: $UU^\top=ZZ^\top$ with $X^\top U\succeq 0$ (Chen–Li §4.2.1)Proved

  Aug 2026

• Decomposition of the auxiliary function $K$ (Ge–Jin–Zheng Lemma 7; Chen–Li Lemma 4.7)Proved

  Aug 2026

• QuantumParallelRepetition.entangledValue_tendsto_zeroProved

  Aug 2026

• QuantumParallelRepetition.entangledValue_polynomial_decayProved

  Aug 2026

• QuantumParallelRepetition.entangledValue_exponential_decayProved

  Aug 2026

• Repeated entangled value is computed by a game on Fin alphabetsProved

  Aug 2026

• Entangled value is computed by a game on Fin alphabetsProved

  Aug 2026

• Relabelling commutes with parallel repetitionProved

  Aug 2026

• Relabelled games have equal entangled valueProved

  Aug 2026

• Relabelling preserves the winning probabilityProved

  Aug 2026

• Relabelling preserves outcome probabilitiesProved

  Aug 2026

• Higher-order reward necessity: order-$(N-1)$ value locality forces separabilityProved

  Aug 2026

• Agent-wise marginal independence characterizes separable joint transitionsProved

  Aug 2026

• Shared rewards add a reward-entanglement term to the error against the marginalized local value functionsProved

  Aug 2026

• Entrywise decomposition error against the marginalized local value functions under the ATV measureProved

  Aug 2026

• Markov entanglement bounds the decomposition error against the marginalized local value functionsProved

  Aug 2026

Posted 50

• Theorem 2(iv), corrected: uniform ergodicity vs. $\varphi$-mixing (Doeblin's full-measure form)Open

  Aug 2026

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

  Aug 2026

• Theorem 2.17 -- avoiding zero for $r$ stepsOpen

  Aug 2026

• Lemma 2.18 -- the reflection principle on $\mathbb{Z}$Open

  Aug 2026

• Proposition 2.4 -- the coupon collector's tail boundOpen

  Aug 2026

• Proposition 2.3 -- the coupon collector's expected timeOpen

  Aug 2026

• Proposition 2.1 -- gambler's ruinOpen

  Aug 2026

• Proposition 2.13 -- irreducibility of a group walkOpen

  Aug 2026

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

  Aug 2026

• Proposition 1.22 -- the time reversal of a chainOpen

  Aug 2026

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

  Aug 2026

• Proposition 1.19 -- detailed balance implies stationarityOpen

  Aug 2026

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

  Aug 2026

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

  Aug 2026

• Proposition 1.14 -- existence of a positive stationary distributionOpen

  Aug 2026

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

  Aug 2026

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

  Aug 2026

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

  Aug 2026

• The gambler's ruin chain, the coupon collector, and simple random walk on $\mathbb{Z}$Definition

  Aug 2026

• Trajectories, return times, and hitting times of a finite chainDefinition

  Aug 2026

• Finite Markov chains: transition matrices, stationarity, irreducibility, period, reversibilityDefinition

  Aug 2026

• Barrier method: $O(\sqrt{m}\log(1/\varepsilon))$ Newton stepsProved

  Aug 2026

• Barrier method: $O(\sqrt{m}\log(1/\varepsilon))$ Newton stepsOpen

  Aug 2026

• Newton complexity for self-concordant functionsProved

  Aug 2026

• Domain-confined backtracking line search and damped Newton runDefinition

  Aug 2026

• Generalized hinging-hyperplane representation of CPWL functionsProved

  Aug 2026

• Finite affine maxima reduce to $(n+1)$-argument hingesProved

  Aug 2026

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

  Aug 2026

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

  Aug 2026

• $\varphi$-mixing CLT: $E Y^2 < \infty$, $\sum \sqrt{\varphi(n)} < \infty$ (Jones Thm 8)Open

  Aug 2026

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

  Aug 2026

• $\rho$-mixing CLT: $E Y^2 < \infty$, $\sum \rho(n) < \infty$ (Jones Thm 7)Open

  Aug 2026

• Geometric ergodicity CLT under $E_\pi[f^2 \log^+|f|] < \infty$ (Jones Cor 3)Open

  Aug 2026

• Doukhan–Massart–Rio CLT: $\alpha(n) = O(a^n)$, $E[Y^2\log^+|Y|] < \infty$ (Jones Thm 6)Open

  Aug 2026

• Chan–Geyer and polynomial-ergodicity CLTs (Jones Cor 2)Open

  Aug 2026

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

  Aug 2026

• Ibragimov–Linnik CLT, moment case: $E|Y|^{2+\delta} < \infty$, $\sum \alpha(n)^{\delta/(2+\delta)} < \infty$ (Jones Thm 5(ii))Open

  Aug 2026

• Ibragimov–Linnik CLT, bounded case: $|Y| < B$ a.s., $\sum \alpha(n) < \infty$ (Jones Thm 5(i))Open

  Aug 2026

• Chen characterization: CLT $\iff$$\sqrt{n}\bar f_n$ bounded in probability (Jones Thm 4)Open

  Aug 2026

• Strongly mixing stationary sequences: CLT $\iff$$\{S_n^2/\sigma_n^2\}$ uniformly integrable (Jones Thm 3)Open

  Aug 2026

• Uniform ergodicity $\iff$ uniform ($\varphi$-) mixing, with exponential rate (Jones Thm 2(iv))Disproved

  Aug 2026

• Geometric ergodicity + detailed balance $\Rightarrow$ exponential $\rho$-mixing (Jones Thm 2(iii))Open

  Aug 2026

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

  Aug 2026

• Harris ergodic chains are strongly mixing: $\alpha(n) \to 0$ (Jones Thm 2(i))Proved

  Aug 2026

• CLT under polynomial drift: $\Delta V \le -dV^\tau + b\,\mathbb{1}_C$, $|f| \le V^{\tau+\eta-1}$ (Jones Thm 1(ii))Open

  Aug 2026

• CLT under geometric drift: $\Delta V \le -dV + b\,\mathbb{1}_C$, $f^2 \le V$ (Jones Thm 1(i))Open

  Aug 2026

• Strict stationarity; the $\alpha$-, $\rho$-, $\varphi$-mixing coefficients; asymptotic varianceDefinition

  Aug 2026

• Small sets (minorization) and the geometric / polynomial drift conditionsDefinition

  Aug 2026

• Harris ergodicity; geometric, uniform, and polynomial ergodicityDefinition

  Aug 2026

• Chain law from an initial distribution, sample averages, and the CLT propertyDefinition

  Aug 2026