I agree with the rest of the reviewers here, the name shouldn't have been Random Walk, instead it should have been Random Dating, as that's what the main character does all the freaking time.
Random Walk stars main character Yuka. She's had a few boyfriends already, and now she's a first year in high school. She meets a random boy, and decides she likes him. She asks to be his girlfriend, he says yes. Chapters go on, and they break up. Yuka meets a new boy and decides she likes him. They date, they break up. Rinse and repeat for 3 more times.
Random Walk offers almost nothing new. The art is bland and the main character's design gets lost in the rest of the shoujo genre art. She's nothing special. She's got a rather flat personality, and the only thing we see her 'liking' apart from boys, is taking pictures. All the boys have zero personality too, and very questionable morals.
Since the characters are so bland, you don't really feel like reading the rest anymore, since you don't care what happens to any of them. Sure the manga tries to portray a more realistic way of teen dating, since I've known plenty of girls myself who were exactly like Yuka (randomly dating guys they don't know, and breaking up within 3 days to a week), but there was one thing that really bothered me about this realistic portrayal. There was no jealousy. You'd think that since they're teenagers, and they've dated plenty of times before, that their current girlfriend or boyfriend would get jealous of their past relationships, or would get jealous if they saw them with another girl/boy.
But there's absolutely no jealousy in this manga. The only 'conflict' this manga has is that you know they're going to break up, and you're skimming through the pages, waiting for this to happen. I'm also very surprised that nothing else happened besides kissing. Where's the sexual tension when you're in a relationship? Like the jealousy part, it's non-existent.
I wouldn't recommend reading Random Walk. It's not really enjoyable, with bland characters who you don't care about, little to no plot, and nothing ever progresses further than kissing. That, and the ending was cut very short.