  When we try to solve a system of linear equations, we can consider a simple
iterative algorithm in which an equation including only one variable is chosen
at each step, and the variable is fixed to the value satisfying the equation.
The dynamics of this algorithm is captured by the peeling algorithm. Analyses
of the peeling algorithm on random hypergraphs are required for many problems,
e.g., the decoding threshold of low-density parity check codes, the inverting
threshold of Goldreich's pseudorandom generator, the load threshold of cuckoo
hashing, etc. In this work, we deal with random hypergraphs including
superlinear number of hyperedges, and derive the tight threshold for the
succeeding of the peeling algorithm. For the analysis, Wormald's method of
differential equations, which is commonly used for analyses of the peeling
algorithm on random hypergraph with linear number of hyperedges, cannot be used
due to the superlinear number of hyperedges. A new method called the evolution
of the moment generating function is proposed in this work.

Discrete Mathematics