While there seem to be too many different variables in the life of a teen (other than low self-esteem and violent acts), researchers have made very poignant claims as to the correlation of the two.
As a side note, come other variables which exist when regarding violence and self-esteem are drugs, alcohol, socio-economic status, jealousy, and societal influence.
Outside of that, teens with low self-esteem have been seen to be more violent based upon a combination of increased anxieties. Therefore, teens who act violently do so given they are faced with situations where they cannot control their anxieties in any other fashion than through violent acts.
Another aspect of the co-morbidity of low self-esteem and violence is the fact that teens with low self-esteem are more likely to engage in behaviors which will boost their self-esteem. (Fighting (violent) and winning (boost in self-esteem) can make teens more likely to act violently given the raised self-esteem which comes from the violent act.