# Dr. Yilun Shang

**Committee:**International Scientific Committee of Mathematical and Computational Sciences

**University:**Tongji University

**Department:**Department of Mathematical Sciences

**Research Fields:**Random Graph Theory, Complex Networks, Wireless Networks, Synchronization and Consensus Problems in Multi-agent Systems, Cyber Security

## Publications

##### 6 On the Hierarchical Ergodicity Coefficient

**Authors:**
Yilun Shang

**Abstract:**

In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.

**Keywords:**
partition,
stochastic matrix,
ergodicity coefficient

##### 5 The Sizes of Large Hierarchical Long-Range Percolation Clusters

**Authors:**
Yilun Shang

**Abstract:**

**Keywords:**
Component,
Phase Transition,
percolation,
hierarchical lattice

##### 4 Likelihood Estimation for Stochastic Epidemics with Heterogeneous Mixing Populations

**Authors:**
Yilun Shang

**Abstract:**

**Keywords:**
maximum likelihood,
statistic inference,
epidemicmodel,
heterogeneous mixing

##### 3 The Giant Component in a Random Subgraph of a Weak Expander

**Authors:**
Yilun Shang

**Abstract:**

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

**Keywords:**
percolation,
Expander,
random graph,
subgraph,
giant component

##### 2 On the Central Limit Theorems for Forward and Backward Martingales

**Authors:**
Yilun Shang

**Abstract:**

**Keywords:**
Central Limit Theorem,
martingale difference sequence,
backward martingale

##### 1 Topological Properties of an Exponential Random Geometric Graph Process

**Authors:**
Yilun Shang

**Abstract:**

**Keywords:**
Wireless Network,
Connectivity,
autoregressive process,
markovian,
degree,
random geometric graph