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Jinyoung Park and Huy Tuan Pham Prove the Kahn-Kalai Conjecture（图）
Kahn-Kalai Conjecture probabilistic combinatorics phase transition the expectation threshold conjecture
2022/4/25
Past Member (2020–21) Jinyoung Park, a Szegö Assistant Professor at Stanford University, and Huy Tuan Pham, a Stanford Ph.D. student, proved the Kahn-Kalai Conjecture, a central problem in probab...
AN ERGODIC ACTION OF THE OUTER AUTOMORPHISM GROUP OF A FREE GROUP
OUTER AUTOMORPHISM ERGODIC ACTION
2015/9/29
For n > 2, the action of the outer automorphism
group of the rank n free group Fn on Hom(Fn, SU(2))/SU(2) is
ergodic with respect to the Lebesgue measure class.
IDEAL TRIANGLES IN EUCLIDEAN BUILDINGS AND BRANCHING TO LEVI SUBGROUPS
EUCLIDEAN BUILDINGS AND BRANCHING mathematics
2015/9/29
Let G denote a connected reductive group, de ned and split over Z, and
let M G denote a Levi subgroup. In this paper we study varieties of geodesic
triangles with xed vector-valued side-lengths ...
We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SLn(Z/kZ) with respect to a standard two-element generating set, is at most a constant times n2 ln k. This answers a ques...
HIGHER-LEVEL CANONICAL SUBGROUPS IN ABELIAN VARIETIES
ABELIAN VARIETIES CANONICAL SUBGROUPS
2015/7/6
An abeloid space over a rigid space S over a non-archimedean field k is a proper
smooth S-group A → S with connected fibers. Relative ampleness (in the sense of [C3]) gives a good notion
...
We develop the relative theory of reductive group schemes,
using dynamic techniques and algebraic spaces to streamline the original development in SGA3.
Gauss Sum Combinatorics and Metaplectic Eisenstein Series
Metaplectic Eisenstein Series Gauss Sum Combinatorics
2015/7/6
For metaplectic covers of these groups, the Whittaker models may or may not be
unique. Gelbart and Piatetski-Shapiro considered the representations of the double
cover of SL2 that have unique Whitta...
Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory
Type A Combinatorial Theory Dirichlet Series
2015/7/6
Speci cally, two distinct versions of the Gelfand-Tsetlin de nition were given. It
is not apparent that they are equal. Either of these de nitions is purely local in that
it speci es the p-part of t...
Conditional Optimal Composite Design.
Combinatorics and Statistical Inferencing D-Optimal Experimental Designs with Covering Array Attributes
Combinatorics Statistical Inferencing
2015/3/18
Wh ile D-O p tim al exp er im ental d es ign s ar e u s ed w ith gr eat f r equ en cy in s u r f ace
r es p on s e an alys is th ey als o offer a m ech an is m to s cr een f actor s an d f actor inte...
通过随机矩阵方法识别、消除极端或非无关抽样样本, 提高Markowitz 模型的参数估计精度, 改进应用Markowitz 模型的效果;同时, 针对抽样不足的情况, 使用Bootstrap 方法较好地解决了该问题.
A recent question in generalized Ramsey theory is that for fixed positive integers $s\leq t$, at least how many vertices can be covered by the vertices of no more than $s$ monochromatic members of the...
Lattice-point generating functions for free sums of convex sets
Lattice-point generating functions free sums of convex sets Combinatorics
2012/7/11
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
Extremal values on the eccentric distance sum of trees
Eccentric distance sum Domination number Leaves Bipartition
2012/7/11
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
On the existence and number of $(k+1)$-kings in $k$-quasi-transitive digraphs
digraph k-king quasi-transitive digraph k-quasi-transitive digraph
2012/6/30
Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \...