Local extrema in random trees
The number of local maxima (resp., local minima) in a tree T∈𝒯n rooted at r∈[n] is denoted by Mr(T) (resp., by mr(T)). We find exact formulas as rational functions of n for the expectation and variance of M1(T) and mn(T) when T∈𝒯n is chosen randomly according to a uniform distribution. As a conseque...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3867 |
| Summary: | The number of local maxima (resp., local minima) in a tree T∈𝒯n rooted at r∈[n] is denoted by Mr(T) (resp., by mr(T)). We find exact formulas as rational functions of n for the expectation and
variance of M1(T) and mn(T) when T∈𝒯n is chosen
randomly according to a uniform distribution. As a consequence,
a.a.s. M1(T) and mn(T) belong to a relatively small interval
when T∈𝒯n. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |