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A dedicated interest (or special interest as defined by non-autistics) is a deep and abiding curiosity and fascination about a particular topic. The topic could be anything, and could range from a very broad field, such as physics or ocean life, to as narrow a subject as a single species of mushroom or an individual episode of a cartoon.
Dedicated interests often come and go over a person's lifetime and may last a few months to many years. Some people have several dedicated interests at a time while some have only one, and sometimes dedicated interests that had faded away can come back and be a central focus again.
The name dedicated interest is somewhat recent, but is gaining popularity among autistic academics who are trying to break away from the language of pathology (the viewpoint that autism is aberrant rather than a natural and common difference) to build language that celebrates neurodiversity. Under the pathology paradigm, dedicated interests are labelled special interests — a term which is coming to be seen as patronising, especially when applied to adults.
Another proposed alternative is autistic area of expertise (AAE). 
Any others? I always used passion, vocation, and obsession before realising I was autistic...
Distinction from hobbies
What distinguishes a dedicated interest from a plain interest or a hobby is its intensity and the distinctive way a person interacts with it. A dedicated interest draws your attention so strongly that you feel like you never get tired of it. You want to spend time on it every day; you might wake up thinking about it and still be thinking about it as you fall asleep. You might go looking for more information or reread your favorite passages about it whenever you get a free moment. It may be an important part of how you organize your understanding of the world, a framework you relate all your other knowledge to. It may fill you with a deep sense of satisfaction and happiness to engage with it, and you may feel frustrated and overwhelmed by the world when you have to spend too much time away from it.
What's the difference between a hyperfixation and dedicated interest?
See also: hyperfixation
Dedicated interests are often a source of great joy and fulfillment in life for Autistic people, and it's important for Autistic well-being to engage with and encourage them. Some people build careers around their dedicated interests, but that's not the only way to make a place for them in your life. Dedicated interests that no one else understands, that you pursue only for your own satisfaction, are every bit as valuable. Spending time on dedicated interests can be a good way to relax and get some relief from an overwhelming world. And bringing joy is enough reason to celebrate their existence.
Bias in autism research
As doctors and scientists originally only looked for autism in white boys, they incorrectly believed — and sometimes still believe — that dedicated interests can only be in things like trains, planes, and math. It's just as common for people to have dedicated interests in horses, literature, and art. It's not about what you're interested in, so much as how deeply you're interested in it.
Let's add a few varied examples of dedicated interests, emphasising how it's not just stereotypical ones such as trains (although that's fine too), preferably with off-site links to photos of people's collections.