This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.

This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.

In this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value and identify the partial differential equation to which it is related. This is the first time that such equation is found to have a relation with game theory. Moreover, our analysis relies on comparison and viscosity tools, in contrast to probabilistic arguments which are more common in the literature. The work also includes a review of the infinity Laplacian and its connection to the classical random Tug-of-War game, as well as an introduction to the theory of viscosity solutions. Furthermore, some explicit examples of the new game are considered.

Homer grows up knowing he looks different than most kids in his neighborhood. Although both his parents are African American, his appearance more closely resembles a Caucasian. As he struggles to fit in with others in his African American race, Homer faces prejudice and bullying by those who brand him the white kid, until he decides to fight back, transforming himself and his attitude forever. On his wayward journey to removing himself from his surroundings, Homer feels his looks are a curse which sets off a series of horrific events that test all his emotions. To others it seems as though Homer has been given all the keys to unlock the American Dream. Unfortunately, they are unaware of his sins as a youth. As Homer relives his experiences, joys, and challenges through the metaphorical structure of eighteen holes of golf, he shines a light on his determined quest to overcome his outcast label, accept his mixed heritage, seek forgiveness, andmore importantlylove himself. Sins of a Mulatto Outcast tells the compelling tale of one mans struggles to embrace his uniqueness in order to achieve happiness in life.

mpulsive, YES. Irresponsible, SURE. Necessary, PROBABLY. Going to end badly, most likely. Does any of that matter to me, no. I decided that I can't please everyone so this week my only goal is to please me. I'm a selfish cow but I can't seem to help it. I'm Clara Lord. I own Bloodline's Tattoo Parlor, have a filthy mouth, no filter and a really strong objection to bossy idiots, pet names and wealthy men. You will hate me, love me or love to hate me but either way, it doesn't matter. Everything I touch turns to crap and it's all my fault. See, I lived through hell. Then I escaped hell and carefully spent the next eight years crafting a perfect little life until Domini Napoli screwed it all up. Now nothings right. Everything's wrong and all my secrets are coming out. Obviously, I have to fix it, my life, the problem is I don't really trust anyone and I don't know how. Dominic baffles me. Sawyer adores me. Amanda and Marg try to keep me in line and I live for Allie. This whole thing is a cluster F***. I want them both in different ways but I have Alliecat to protect in the mix. I keep thinking the only way out of this is to take Allie and run...again. Leave both men behind and go back to Allie and Clara take on the world...is thirty-three too old to do that now? It didn't seem so bad at twenty-four but to have to do all that work again... crap.