稀疏随机点积图中三角形数量的极限定理

Limit laws for the number of triangles in the sparse random dot product graphs

研究了具有随机顶点向量的稀疏随机点积图中三角形数量的渐近行为,其中顶点之间的边概率与顶点向量的乘积成某种比例关系.当顶点数趋于无穷时,证明了三角形数量的渐近分布收敛到泊松分布.

It research the asymptotic behavior for the number of triangles in a sparse random dot product graphs with random vertex vectors,in which the edge probabilities between vertices are proportional to the product of vertex vectors.When the number of vertices tends to infinity,we prove that the asymptotic distribution of the number of trianglesconverges to a Poisson distribution.