随机图上模型的重构

随机着色的重构

Reconstruction of Random Colourings

重建问题已经在包括生物学、信息论和统计物理学的许多背景下被研究。本文研究了大$k$的$Δ$ -ary树上随机$k$ -着色的重建问题.巴特纳加尔等当使用$Δ\leq \frac12 k\log k - o(k\log k)$时显示无重建，当使用$Δ\geq k\log k + o(k\log k)$时显示重建。我们收紧了这一结果，并显示了当$Δ\leq k[\log k + \log \log k + 1 - \ln 2 -o(1)]$时的非重建和当$Δ\geq k[\log k + \log \log k + 1+o(1)]$时的重建。

Approximate trace reconstruction of random strings from a constant number of traces

In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace reconstruction, the goal is to reconstruct an approximation $\widehat{x}$ of $x$ which is close (within $εn$) to $x$ in edit distance. We show that for most strings $x$, this is possible with high probability using only a constant number of traces. Crucially, this constant does not grow with $n$, and only depends on the deletion probability and $ε$.

依赖平稳随机变量紧支撑的拓扑重建

Topological reconstruction of compact supports of dependent stationary random variables

本文提出了一种依赖平稳随机变量紧支撑的拓扑重建方法，并通过示例展示了其在莫比乌斯马尔可夫链中的应用。

Reconstruction of a multidimensional scenery with a branching random walk

In this paper we consider a d-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it is seeing. We show that we can a.s. reconstruct the scenery up to equivalence from the color record of all the particles. For this we assume that the scenery has at least 2d + 1 colors which are i.i.d. with uniform probability. This is an improvement in comparison to [22] where the particles needed to see at each time a window around their current position. In [11] the reconstruction is done for d = 2 with only one particle instead of…

Geometry of log-concave Ensembles of random matrices and approximate reconstruction

We study the Restricted Isometry Property of a random matrix $Γ$ with independent isotropic log-concave rows. To this end, we introduce a parameter $Γ_{k,m}$ that controls uniformly the operator norm of sub-matrices with $k$ rows and $m$ columns. This parameter is estimated by means of new tail estimates of order statistics and deviation inequalities for norms of projections of an isotropic log-concave vector.

随机行走上的场景重建

Scenery Reconstruction for Random Walk on Random Scenery Systems

本文研究了在随机行走中面对对手篡改记录的情况下，如何仍能重建大部分场景的性质。