The height and width of simple trees

The height and width of simple trees P. Chassaing 1 , J.F. Marckert 1 , M. Yor 2 . The limit law of the couple height-width for simple trees can be seen as a consequence of deep results of Aldous, Drmota and Gittenberger, and Jeulin. We give here an elementary proof in the case of binary trees. 1 Introduction Let Z i (t) denote the number of nodes at distance i from the root of a rooted tree t. The prole of the tree t is the sequence (Z i (t)) i0 . The width w(t) and height h(t) of the tree t are dened by: w(t) = max i fZ i (t)g; h(t) = maxfijZ i (t) > 0g: Let T (n) B denote the set of binary trees with n leaves (2n 1 nodes), endowed with the uniform probability, and let H (n) B (resp. W (n) B ) be the restriction of h (resp. w) to T (n) B .

• rst walk


• galton watson tree


• between height


• standard normalized


• brownian excursion


• jeulin's description


• normalized brownian


• excursion - binary tree