Some of the above comments are almost true, but not quite.
MOST people are put on the acceptance range this time of year. Do not take this as a slap in the face. However, while it is possible for it to happen earlier, most movement from the acceptance range happens once May rolls around.
So the moral of the story is- send in LOI's, updates, etc. Don't be psycho about it- something every six weeks or so now, maybe more often as it gets closer to May. Don't be discouraged if you don't hear anything back- you usually won't. Don't worry- they're getting the stuff.
If you want to go here more than any other med school, let them know, and let them know why. Make sure you explain what it is about Tulane that you think makes it the perfect place for you. And be aware that the admissions people have pretty good bull$hit filters. If you're just trying to get in somewhere and you don't know much about Tulane, they'll know. But if you honestly want to come here more than anywhere else, they'll be receptive to that.
Good luck!