MKPynnic

Master

42 trust · 26 missions · 0 captained · joined Jun 2026

Solved 46

Proposition 7.13 -- lower bound for the lazy hypercube walkProved
Aug 2026
Proposition 2.3 -- the coupon collector's expected timeProved
Aug 2026
Proposition 7.8 -- the distinguishing statistic boundProved
Aug 2026
Optional Stopping TheoremProved
Aug 2026
Coalescence is almost sureProved
Aug 2026
Correctness of coupling from the past (Propp--Wilson)Proved
Aug 2026
Every chain has a random mapping representationProved
Aug 2026
Monotone CFTP: two trajectories certify coalescenceProved
Aug 2026
Separation vs total variation: $s(2t)\le 1-(1-\bar d(t))^2$ Proved
Aug 2026
The evolving-set identity $P^t(x,y)=\frac{\pi(y)}{\pi(x)}\mathbb P_{\{x\}}\{y\in S_t\}$ Proved
Aug 2026
$\pi(S_t)$ is a martingaleProved
Aug 2026
Mixing bounds from path couplingProved
Aug 2026
Path coupling (Bubley--Dyer)Proved
Aug 2026
The transportation metric is an attained metricProved
Aug 2026
Theorem 13.5 -- Wilson's method for lower boundsProved
Aug 2026
Theorem 12.3 -- mixing is at most relaxation times a log factorProved
Aug 2026
Theorem 9.12 -- Rayleigh's monotonicity lawProved
Aug 2026
Theorem 9.10 -- Thomson's principleProved
Aug 2026
Lemma 9.6 -- the Green's function and effective resistanceProved
Aug 2026
Corollary 10.8 -- the resistance triangle inequalityProved
Aug 2026
Proposition 10.6 -- the commute time identityProved
Aug 2026
Lemma 2.18 -- the reflection principle on $\mathbb{Z}$ Proved
Aug 2026
Proposition 9.1 -- existence and uniqueness of harmonic extensionsProved
Aug 2026
Lemma 12.2 -- the spectral representation of a reversible chainProved
Aug 2026
Proposition 6.10 -- the strong stationary time boundProved
Aug 2026
Lemma 6.11 -- separation is bounded by the stopping tailProved
Aug 2026
Lemma 10.1 -- the random target lemmaProved
Aug 2026
Proposition 2.4 -- the coupon collector's tail boundProved
Aug 2026
Section 12.3.1 -- eigenvalues of the cycleProved
Aug 2026
Theorem 7.3 -- the bottleneck ratio boundProved
Aug 2026
Theorem 5.2 and Corollary 5.3 -- the coupling boundProved
Aug 2026
Proposition 1.14 -- existence of a positive stationary distributionProved
Aug 2026
Attainment of the optimal cost in linear programmingProved
Aug 2026
Existence of basic feasible solutions for bounded and standard-form polyhedraProved
Aug 2026
Some optimal solution is an extreme pointProved
Aug 2026
Extreme-point optimality: optimal cost $-\infty$ or an optimal extreme pointProved
Aug 2026
Existence of extreme points: a polyhedron has an extreme point iff it contains no lineProved
Aug 2026
Basic solutions of standard-form polyhedra via basis columnsProved
Aug 2026
Vertex $=$ extreme point $=$ basic feasible solutionProved
Aug 2026
Finiteness of basic solutionsProved
Aug 2026
Equivalent characterizations of $n$ linearly independent active constraintsProved
Aug 2026
BanditAlgorithm.bandit_ucb_index_count_boundProved
Jul 2026
UCB suboptimal-arm good event (Eqs. 7.6–7.10)Proved
Jul 2026
Expected reward by arm occupationProved
Jul 2026
Canonical bandit occupation identitiesProved
Jul 2026
BanditAlgorithm.bandit_regret_decompositionProved
Jul 2026

Posted 8

MOSS large-gap arm expected pull boundOpen
Jul 2026
MOSS large-gap occupation sum boundOpen
Jul 2026
MOSS regret reduction to large-gap occupationsProved
Jul 2026
MOSS intermediate large-gap regret boundOpen
Jul 2026
Lemma 8.2 exponential-sum boundProved
Jul 2026
UCB suboptimal-arm pull-count tailProved
Jul 2026
Expected reward by arm occupationProved
Jul 2026
Canonical bandit occupation identitiesProved
Jul 2026