On the topological Properties of the One Dimensional Exponential Random Geometric Graph

Tail bounds for sums of geometric and exponential variables

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

Super-exponential extinction time of the contact process on random geometric graphs

In this paper, we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connecting radius tending to infinity. We obtain that for any infection rate $λ>0$, the contact process on these graphs survives a time super-exponential in the number of vertices.

Vertex Degree of Random Geometric Graph on Exponentially Distributed Points

Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if and only if edge distance between them is greater then $y$, i.e, $\|X_i-X_j\| \leq y.$ Almost-sure asymptotic rates of convergence/divergence are obtained for the minimum and maximum vertex degree of the random geometric graph, as the number of vertices becomes large $n,$ and the edge distance varies with the number of vertices.

Limit shapes for inhomogeneous corner growth models with exponential and geometric weights

We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution $a_i+b_j$ and the parameter of the geometric distribution $a_i b_j$ at site $(i, j)$, where $(a_i)_{i \ge 1}$ and $(b_j)_{j \ge 1}$ are jointly ergodic random sequences. We identify the shape function in terms of a simple variational problem, which can be solved explicitly in some special cases.

使随机变量对称化需要多少随机性？

Symmetrization resistance for exponential and geometric distributions

研究使随机变量对称化所需的随机性，通过指数卷积的微分反演公式及离散差分算子等方法，对指数分布和几何分布建立对称化抗性结果，给出熵和方差对称化抗性分布新例，且表明特定条件下等式成立。

Independence of Linear Statistics with Random Coefficients and Characterizations of Geometric and Poisson Distributions

There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear statistics independence is also a characterization of Poisson law. Keywords: geometric distribution; exponential distribution; Poisson distribution; linear forms; random coefficients