The black walnut tree is definitely opposed to diversity. It employs chemical warfare to try and prevent anything other than another walnut tree from growing in its immediate vicinity. In the plant world this type of warfare is called allelopathy and the chemical inhibitor specifically produced by the black walnut is juglone. Unfortunately tomato plants are especially sensitive to juglone. A large walnut tree even 60 feet away could have a negative impact on a tomato plants growth. Affected plants will show signs of wilting, and the leaves will turn yellow. Growth will definitely be stunted causing the plant to eventually die.
The toxic chemical is in all parts of the tree: its trunk, limbs, twigs, roots, leaves, bark, and nuts. Using free mulch of an unknown origin may not be such a good idea for it may contain shredded black walnut.